Fundamentals of Physics

David Halliday, Robert Resnick, Jearl Walker

Chapter 5

Force and Motion-I - all with Video Answers

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Chapter Questions

Problem 1

Only two horizontal forces act on a $3.0 \mathrm{~kg}$ body that can move over a frictionless floor. One force is $9.0 \mathrm{~N}$, acting due east, and the other is $8.0 \mathrm{~N}$, acting $62^{\circ}$ north of west. What is the magnitude of the body's acceleration?

Averell Hause

Averell Hause

Carnegie Mellon University

Problem 2

Two horizontal forces act on a $2.0 \mathrm{~kg}$ chopping block that can slide over a frictionless kitchen counter, which lies in an $x y$ plane. One force is $\vec{F}_{1}=(3.0 \mathrm{~N}) \hat{\mathrm{i}}+(4.0 \mathrm{~N}) \hat{\mathrm{j}}$. Find the acceleration of the
chopping block in unit-vector notation when the other force is
(a) $\vec{F}_{2}=(-3.0 \mathrm{~N}) \hat{\mathrm{i}}+(-4.0 \mathrm{~N}) \hat{\mathrm{j}}$
(b) $\vec{F}_{2}=(-3.0 \mathrm{~N}) \hat{\mathrm{i}}+(4.0 \mathrm{~N}) \hat{\mathrm{j}}$
and $(\mathrm{c}) \vec{F}_{2}=(3.0 \mathrm{~N}) \hat{\mathrm{i}}+(-4.0 \mathrm{~N}) \hat{\mathrm{j}}$

Kathleen Tatem

Numerade Educator

Problem 3

If the $1 \mathrm{~kg}$ standard body has an acceleration of $2.00 \mathrm{~m} / \mathrm{s}^{2}$ at $20.0^{\circ}$ to the positive direction of an $x$ axis, what are (a) the $x$ component and (b) the $y$ component of the net force acting on the body, and (c) what is the net force in unit-vector notation?

Prabhu Ramji

Numerade Educator

Problem 4

While two forces act on it, a particle is to move at the constant velocity $\vec{v}=(3 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}-(4 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}$. One
of the forces is $\vec{F}_{1}=(2 \mathrm{~N}) \hat{\mathrm{i}}+$
$(-6 \mathrm{~N}) \hat{\mathrm{j}} .$ What is the other force?

Kathleen Tatem

Numerade Educator

Problem 5

Three astronauts, propelled by jet backpacks, push and guide a $120 \mathrm{~kg}$ asteroid toward a processing dock, exerting the forces shown in Fig. $5-29$, with $F_{1}=32 \mathrm{~N}, F_{2}=55 \mathrm{~N}$,
$F_{3}=41 \mathrm{~N}, \quad \theta_{1}=30^ {\circ}$, and $\theta_{3}=60^{\circ} .$
What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction relative to the positive direction of the $x$ axis?

Prabhu Ramji

Numerade Educator

Problem 6

In a two-dimensional tug-ofwar, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of Fig. $5-30 .$ The tire remains stationary in spite of the three pulls Alex pulls with force $\vec{F}_{A}$ of magnitude $220 \mathrm{~N}$, and Charles pulls with force $\vec{F}_{C}$ of magnitude $170 \mathrm{~N}$. Note that the direction of $\vec{F}_{C}$ is not given. What is the magnitude of Betty's force $\vec{F}_{B} ?$

Prabhu Ramji

Numerade Educator

Problem 7

There are two forces on the $2.00 \mathrm{~kg}$ box in the overhead view of Fig. 5-31, but only one is shown. For $F_{1}=20.0 \mathrm{~N}, a=12.0 \mathrm{~m} / \mathrm{s}^{2}$, and $\theta=30.0^{\circ}$,
find the second force (a) in unit-vector notation and as (b) a magnitude and
(c) an angle relative to the positive direction of the $x$ axis.

Averell Hause

Carnegie Mellon University

Problem 8

A $2.00 \mathrm{~kg}$ object is subjected to three forces that give it an acceleration $\vec{a}=-\left(8.00 \mathrm{~m} / \mathrm{s}^{2}\right) \hat{\mathrm{i}}+\left(6.00 \mathrm{~m} / \mathrm{s}^{2}\right) \hat{\mathrm{j}} .$ If
two of the three forces are $\vec{F}_{1}=(30.0 \mathrm{~N}) \hat{\mathrm{i}}+(16.0 \mathrm{~N}) \hat{\mathrm{j}}$ and $\vec{F}_{2}=$
$-(12.0 \mathrm{~N}) \hat{\mathrm{i}}+(8.00 \mathrm{~N}) \hat{\mathrm{j}}$, find the third force.

Kathleen Tatem

Numerade Educator

Problem 9

A $0.340 \mathrm{~kg}$ particle moves in an $x y$ plane according to $x(t)=-15.00+2.00 t-4.00 t^{3}$ and $y(t)=25.00+7.00 t-9.00 t^{2}$,
with $x$ and $y$ in meters and $t$ in seconds. At $t=0.700 \mathrm{~s}$, what are (a) the magnitude and (b) the angle (relative to the positive direction of the $x$ axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?

Averell Hause

Carnegie Mellon University

Problem 10

A $0.150 \mathrm{~kg}$ particle moves along an $x$ axis according to $x(t)=-13.00+2.00 t+4.00 t^{2}-3.00 t^{3}$, with $x$ in meters and $t$ in seconds. In unit-vector notation, what is the net force acting on the particle at $t=3.40 \mathrm{~s}$ ?

Kathleen Tatem

Numerade Educator

Problem 11

A $2.0 \mathrm{~kg}$ particle moves along an $x$ axis, being propelled by a variable force directed along that axis. Its position is given by $x=$ $3.0 \mathrm{~m}+(4.0 \mathrm{~m} / \mathrm{s}) t+c t^{2}-\left(2.0 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}$, with $x$ in meters and $t$ in
seconds. The factor $c$ is a constant. At $t=3.0 \mathrm{~s}$, the force on the particle has a magnitude of $36 \mathrm{~N}$ and is in the negative direction of the axis. What is $c$ ?

Prabhu Ramji

Numerade Educator

Problem 12

Two horizontal forces $\vec{F}_{1}$ and $\vec{F}_{2}$ act on a $4.0 \mathrm{~kg}$ disk that slides over frictionless ice, on which an $x y$ coordinate system is laid out. Force $\vec{F}_{1}$ is in the positive direction of the $x$ axis and has a mag. nitude of $7.0 \mathrm{~N}$. Force $\vec{F}_{2}$ has a magnitude of $9.0 \mathrm{~N}$. Figure $5-32$ gives the $x$ component $v_{x}$ of the velocity of the disk as a function of time $t$ during the sliding. What is the angle between the constant directions of forces $\vec{F}_{1}$ and $\vec{F}_{2} ?$

Kathleen Tatem

Numerade Educator

Problem 13

Figure $5-33$ shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude $98 \mathrm{~N}$ on the wall to which it is attached. The tensions in the three shorter cords are $T_{1}=58.8 \mathrm{~N}$, $T_{2}=49.0 \mathrm{~N}$, and $T_{3}=9.8 \mathrm{~N}$. What are the masses of (a) disk $A$, (b) disk $B$, (c) disk $C$, and (d) disk $D^{2}$ ?

Prabhu Ramji

Numerade Educator

Problem 14

A block with a weight of $3.0 \mathrm{~N}$ is at rest on a horizontal surface. A $1.0 \mathrm{~N}$ upward force is applied to the block by means of an attached vertical string. What are the (a) magnitude and (b) direction of the force of the block on the horizontal surface?

Kathleen Tatem

Numerade Educator

Problem 15

(a) An $11.0 \mathrm{~kg}$ salami is supported by a cord that runs to a spring scale, which is supported by a cord hung from the ceiling (Fig. $5-34 a$ ). What is the reading on the scale, which is marked in SI weight units? (This is a way to measure weight by a deli owner.) (b) In Fig. $5-34 b$ the salami is supported by a cord that runs around a pulley and to a scale. The opposite end of the scale is attached by a cord to a wall. What is the reading on the scale? (This is the way by a physics major.) (c) In Fig. $5-34 c$ the wall has been replaced with a second $11.0 \mathrm{~kg}$ salami, and the assembly is stationary. What is the reading on the scale? (This is the way by a deli owner who was once a physics major.)

Averell Hause

Carnegie Mellon University

Problem 16

Some insects can walk below a thin rod (such as a twig) by hanging from it. Suppose that such an insect has mass $m$ and hangs from a horizontal rod as shown in Fig. $5-35$, with angle $\theta=40^{\circ}$. Its six legs are all under the same tension, and the leg sections nearest the body are horizontal. (a) What is the ratio of the tension in each tibia (forepart of a leg) to the insect's weight? (b) If the insect straightens out its legs somewhat, does the tension in each tibia increase, decrease, or stay the same?

Prabhu Ramji

Numerade Educator

Problem 17

In Fig. 5-36, let the mass of the block be $8.5 \mathrm{~kg}$ and the angle $\theta$ be $30^{\circ}$. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the resulting acceleration of the block.

Averell Hause

Carnegie Mellon University

Problem 18

In In April 1974, John Massis of Belgium managed to move two passenger railroad cars. He did so by clamping his teeth down on a bit that was attached to the cars with a rope and then leaning backward while pressing his feet against the railway ties. The cars together weighed $700 \mathrm{kN}$ (about 80 tons). Assume that he pulled with a constant force that was $2.5$ times his body weight, at an upward angle $\theta$ of $30^{\circ}$ from the horizontal. His mass was $80 \mathrm{~kg}$, and he moved the cars by $1.0 \mathrm{~m}$. Neglecting any retarding force from the wheel rotation, find the speed of the cars at the end of the pull.

Kathleen Tatem

Numerade Educator

Problem 19

A $500 \mathrm{~kg}$ rocket sled can be accelerated at a constant rate from rest to $1600 \mathrm{~km} / \mathrm{h}$ in $1.8 \mathrm{~s}$. What is the magnitude of the required net force?

Averell Hause

Carnegie Mellon University

Problem 20

A car traveling at $53 \mathrm{~km} / \mathrm{h}$ hits a bridge abutment. A passenger in the car moves forward a distance of $65 \mathrm{~cm}$ (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of $41 \mathrm{~kg}$ ?

Kathleen Tatem

Numerade Educator

Problem 21

A constant horizontal force $\vec{F}_{a}$ pushes a $2.00 \mathrm{~kg}$ FedEx package across a frictionless floor on which an $x y$ coordinate system has been drawn. Figure $5-37$ gives the package's $x$ and $y$ velocity components versus time $t .$ What are the (a) magnitude and (b) direction of $\vec{F}_{a}$ ?

Prabhu Ramji

Numerade Educator

Problem 22

A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a $y$ axis with an acceleration magnitude of $1.24 g$, with $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$. A $0.567 \mathrm{~g}$ coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what is the coin's acceleration relative to (a) the ground and (b) the customer? (c) How long does the coin take to reach the compartment ceiling, $2.20 \mathrm{~m}$ above the knee? In unit-vector notation, what are (d) the actual force on the coin and (e) the apparent force according to the customer's measure of the coin's acceleration?

Prabhu Ramji

Numerade Educator

Problem 23

Tarzan, who weighs $820 \mathrm{~N}$, swings from a cliff at the end of a $20.0 \mathrm{~m}$ vine that hangs from a high tree limb and initially makes an angle of $22.0^{\circ}$ with the vertical. Assume that an $x$ axis extends horizontally away from the cliff edge and a $y$ axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is $760 \mathrm{~N}$. Just then, what are (a) the force on him from the vine in unit-vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the $x$ axis? What are the (e) magnitude and
(f) angle of Tarzan's acceleration just then?

Averell Hause

Carnegie Mellon University

Problem 24

There are two horizontal forces on the $2.0 \mathrm{~kg}$ box in the overhead view of Fig. $5-38$ but only one (of magnitude $F_{1}=20 \mathrm{~N}$ ) is shown. The box moves along the $x$ axis. For each of the following values for the acceleration $a_{x}$ of the box, find the second force in unit-vector notation: (a) $10 \mathrm{~m} / \mathrm{s}^{2}$, (b) $20 \mathrm{~m} / \mathrm{s}^{2}$
(c) $0,(\mathrm{~d})-10 \mathrm{~m} / \mathrm{s}^{2}$, and $(\mathrm{e})-20 \mathrm{~m} / \mathrm{s}^{2}$

Prabhu Ramji

Numerade Educator

Problem 25

Sunjamming. A "sun yacht" is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Suppose that the spacecraft has a mass of $900 \mathrm{~kg}$ and receives a push of $20 \mathrm{~N}$.
(a) What is the magnitude of the resulting acceleration? If the craft starts from rest, (b) how far will it travel in 1 day and (c) how fast will it then be moving?

Averell Hause

Carnegie Mellon University

Problem 26

The tension at which a fishing line snaps is commonly called the line's "strength." What minimum strength is needed for a line that is to stop a salmon of weight $85 \mathrm{~N}$ in $11 \mathrm{~cm}$ if the fish is initially drifting at $2.8 \mathrm{~m} / \mathrm{s}$ ? Assume a constant deceleration.

Averell Hause

Carnegie Mellon University

Problem 27

An electron with a speed of $1.2 \times 10^{7} \mathrm{~m} / \mathrm{s}$ moves horizontally into a region where a constant vertical force of $4.5 \times$ $10^{-16} \mathrm{~N}$ acts on it. The mass of the electron is $9.11 \times 10^{-31} \mathrm{~kg}$. Determine the vertical distance the electron is deflected during the time it has moved $30 \mathrm{~mm}$ horizontally.

Averell Hause

Carnegie Mellon University

Problem 28

A car that weighs $1.30 \times 10^{4} \mathrm{~N}$ is initially moving at $40 \mathrm{~km} / \mathrm{h}$ when the brakes are applied and the car is brought to a stop in $15 \mathrm{~m}$. Assuming the force that stops the car is constant, find (a) the magnitude of that force and (b) the time required for the change in speed. If the initial speed is doubled, and the car experiences the same force during the braking, by what factors are
(c) the stopping distance and (d) the stopping time multiplied? (There could be a lesson here about the danger of driving at high speeds.)

Averell Hause

Carnegie Mellon University

Problem 29

A firefighter who weighs 712 N slides down a vertical pole with an acceleration of $3.00 \mathrm{~m} / \mathrm{s}^{2}$, directed downward. What are the
(a) magnitude and (b) direction (up or down) of the vertical force on the firefighter from the pole and the (c) magnitude and (d) direction of the vertical force on the pole from the firefighter?

Averell Hause

Carnegie Mellon University

Problem 30

The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick's mass was $0.13 \mathrm{~g}$, its speed before entering the branch was $220 \mathrm{~m} / \mathrm{s}$, and its penetration depth was $15 \mathrm{~mm}$. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick?

Averell Hause

Carnegie Mellon University

Problem 31

A block is projected up a frictionless inclined plane with initial speed $v_{0}=3.50$ plane with initial speed $v_{0}=3.50$ $\mathrm{m} / \mathrm{s}$. The angle of incline is $\theta=32.0^{\circ} .$ (a) How far up the plane does the block go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

Prabhu Ramji

Numerade Educator

Problem 32

Figure $5-39$ shows an overhead view of a $0.0250 \mathrm{~kg}$ lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force $\vec{F}_{1}$ has a magnitude of $6.00 \mathrm{~N}$ and is at $\theta_{1}=30.0^{\circ}$. Force $\vec{F}_{2}$ has a magnitude of $7.00 \mathrm{~N}$ and is at $\theta_{2}=30.0^{\circ}$. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity $\vec{v}=(13.0 \hat{\mathrm{i}}-14.0 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$, and $(\mathrm{c})$ has the
varying velocity $\vec{v}=(13.0 t \hat{\mathrm{i}}-14.0 t \mathrm{j}) \mathrm{m} / \mathrm{s}^{2}$, where $t$ is time?

Prabhu Ramji

Numerade Educator

Problem 33

An elevator cab and its load have a combined mass of $1600 \mathrm{~kg}$. Find the tension in the supporting cable when the cab, originally moving downward at $12 \mathrm{~m} / \mathrm{s}$, is brought to rest with constant acceleration in a distance of $42 \mathrm{~m}$.

Averell Hause

Carnegie Mellon University

Problem 34

In Fig. $5-40$, a crate of mass $m=100 \mathrm{~kg}$ is pushed at con- stant speed up a frictionless ramp $\left(\theta=30.0^{\circ}\right)$ by a horizontal force $\vec{F}$. What are the magnitudes of (a) $\bar{F}$ and (b) the force on the crate from the ramp?

Prabhu Ramji

Numerade Educator

Problem 35

The velocity of a $3.00 \mathrm{~kg}$ particle is given by $\vec{v}=\left(8.00 \hat{i}+3.00 t^{2} \hat{i}\right)$
$\mathrm{m} / \mathrm{s}$, with time $t$ in seconds. At the instant the net force on the particle has a magnitude of $35.0 \mathrm{~N}$, what are the direction (relative to the positive direction of the $x$ axis) of (a) the net force and (b) the particle's direction of travel?

Averell Hause

Carnegie Mellon University

Problem 36

Holding on to a towrope moving parallel to a frictionless ski slope, a $50 \mathrm{~kg}$ skier is pulled up the slope, which is at an angle of $8.0^{\circ}$ with the horizontal. What is the magnitude $F_{\text {rope }}$ of the force on the skier from the rope when (a) the magnitude $v$ of the skier's velocity is constant at $2.0 \mathrm{~m} / \mathrm{s}$ and $(\mathrm{b}) v=2.0 \mathrm{~m} / \mathrm{s}$ as $v$ increases at a rate of $0.10 \mathrm{~m} / \mathrm{s}^{2} ?$

Prabhu Ramji

Numerade Educator

Problem 37

A $40 \mathrm{~kg}$ girl and an $8.4 \mathrm{~kg}$ sled are on the frictionless ice of a frozen lake, $15 \mathrm{~m}$ apart but connected by a rope of negligible mass. The girl exerts a horizontal $5.2 \mathrm{~N}$ force on the rope. What are the acceleration magnitudes of (a) the sled and (b) the girl? (c) How far from the girl's initial position do they meet?

Prabhu Ramji

Numerade Educator

Problem 38

A $40 \mathrm{~kg}$ skier skis directly down a frictionless slope angled at $10^{\circ}$ to the horizontal. Assume the skier moves in the negative direction of an $x$ axis along the slope. A wind force with component $F_{x}$ acts on the skier. What is $F_{x}$ if the magnitude of the skier's velocity is (a) constant, (b) increasing at a rate of $1.0 \mathrm{~m} / \mathrm{s}^{2}$, and $(\mathrm{c})$ increasing at a rate of $2.0 \mathrm{~m} / \mathrm{s}^{2} ?$

Averell Hause

Carnegie Mellon University

Problem 39

A sphere of mass $3.0 \times 10^{-4} \mathrm{~kg}$ is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of $37^{\circ}$ with the vertical. Find (a) the push magnitude and (b) the tension in the cord.
w.40 co A dated box of dates, of mass $5.00 \mathrm{~kg}$, is sent sliding up a frictionless ramp at an angle of $\theta$ to the horizontal. Figure $5-41$ gives,

Prabhu Ramji

Numerade Educator

Problem 40

A dated box of dates, of mass $5.00 \mathrm{~kg}$, is sent sliding up a frictionless ramp at an angle of $\theta$ to the horizontal. Figure $5-41$ gives, as a function of time $t$, the component $v_{x}$ of the box's velocity along an $x$ axis that extends directly up the ramp. What is the magnitude of the normal force on the box from the ramp?

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Bcrypt_Sha256$$2B$12$Koudzt7Vugfesdqzt.Btsohdsno3/5Wc5Bsgjhyqjgxswzij15Z06 Bcrypt_Sha256$$2B$12$Koudzt7Vugfesdqzt.Btsoec1F7Nikxndin/Owbntbjji9Jzcznki

Numerade Educator

Problem 41

Using a rope that will snap if the tension in it exceeds $387 \mathrm{~N}$, you need to lower a bundle of old roofing material weighing $449 \mathrm{~N}$ from a point $6.1 \mathrm{~m}$ above the ground. Obviously if you hang the bundle on the rope, it will snap. So, you allow the bundle to accelerate downward. (a) What magnitude of the bundle's acceleration will put the rope on the verge of snapping? (b) At that acceleration, with what speed would the bundle hit the ground?

Averell Hause

Carnegie Mellon University

Problem 42

Go In earlier days, horses pulled barges down canals in the manner shown in Fig. $5-42 .$ Suppose the horse pulls on the rope with a force of $7900 \mathrm{~N}$ at an angle of $\theta=18^{\circ}$ to the direction of motion of the barge, which is headed straight along the positive direction of an $x$ axis. The mass of the barge is $9500 \mathrm{~kg}$, and the magnitude of its acceleration is $0.12 \mathrm{~m} / \mathrm{s}^{2}$. What are the (a) magnitude and (b) direction (relative to positive $x$ ) of the force on the barge from the water?

Prabhu Ramji

Numerade Educator

Problem 43

In Fig. $5-43$, a chain consisting of five links, each of mass $0.100 \mathrm{~kg}$, is lifted vertically with constant acceleration of magnitude $a=2.50$ $\mathrm{m} / \mathrm{s}^{2}$. Find the magnitudes of (a) the force on link 1 from link $2,($ b) the force on link 2 from link 3 ,
(c) the force on link 3 from link 4 , and (d) the force on link 4 from link 5 . Then find the magnitudes of (e) the force $\vec{F}$ on the top link from the person lifting the chain and (f) the net force accelerating each link.

Vishal Gupta

Numerade Educator

Problem 44

A lamp hangs vertically from a cord in a descending elevator that decelerates at $2.4 \mathrm{~m} / \mathrm{s}^{2} .(\mathrm{a})$ If the tension in the cord is $89 \mathrm{~N}$, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of $2.4 \mathrm{~m} / \mathrm{s}^{2} ?$

Prabhu Ramji

Numerade Educator

Problem 45

An elevator cab that weighs $27.8 \mathrm{kN}$ moves upward. What is the tension in the cable if the cab's speed is (a) increasing at a rate of $1.22 \mathrm{~m} / \mathrm{s}^{2}$ and (b) decreasing at a rate of $1.22 \mathrm{~m} / \mathrm{s}^{2} ?$

Averell Hause

Carnegie Mellon University

Problem 46

An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of $2000 \mathrm{~kg}$. When that occupant drops a coin, its acceleration relative to the cab is $8.00 \mathrm{~m} / \mathrm{s}^{2}$ downward. What is the tension in the cable?

Averell Hause

Carnegie Mellon University

Problem 47

The Zacchini family was renowned for their human-cannonball act in which a family member was shot from a cannon using either elastic bands or compressed air. In one version of the act, Emanuel Zacchini was shot over three Ferris wheels to land in a net at the same height as the open end of the cannon and at a range of $69 \mathrm{~m}$. He was propelled inside the barrel for $5.2 \mathrm{~m}$ and launched at an angle of $53^{\circ} .$ If his mass was $85 \mathrm{~kg}$ and he underwent constant acceleration inside the barrel, what was the magnitude of the force propelling him? (Hint: Treat the launch as though it were along a ramp at $53^{\circ} .$ Neglect air drag.)

Averell Hause

Carnegie Mellon University

Problem 48

In Fig. $5-44$, elevator cabs $A$ and $B$ are connected by a short cable and can be pulled upward or lowered by the cable above cab $A$. Cab $A$ has mass $1700 \mathrm{~kg} ;$ cab $B$ has mass $1300 \mathrm{~kg}$. A $12.0 \mathrm{~kg}$ box of catnip lies on the floor of cab $A$. The tension in the cable connecting the cabs is $1.91 \times 10^{4} \mathrm{~N}$. What is the magnitude of the normal force on the box from the floor?

Prabhu Ramji

Numerade Educator

Problem 49

In Fig. $5-45$, a block of mass $m=5.00 \mathrm{~kg}$ is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude $F=12.0 \mathrm{~N}$ at an angle $\theta=25.0^{\circ} .$ (a) What is the magnitude of the block's acceleration? (b) The force magnitude $F$ is slowly increased. What is its value just before the block is lifted (completely) off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted (completely) off the floor?

Averell Hause

Carnegie Mellon University

Problem 50

In Fig. $5-46$, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The three masses are $m_{A}=30.0 \mathrm{~kg}, \quad m_{B}=40.0 \mathrm{~kg}$, bly is released from rest, (a) what is the tension in the cord connecting $B$ and $C$, and $(b)$ how far does $A$ move in the first $0.250 \mathrm{~s}$ (assuming it does not reach the pulley)?

Prabhu Ramji

Numerade Educator

Problem 51

Figure $5-47$ shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). The arrangement is known as Atwood's machine. One block has mass $m_{1}=1.30 \mathrm{~kg}$; the other has mass $m_{2}=$ $2.80 \mathrm{~kg}$. What are (a) the magnitude of the blocks' acceleration and (b) the tension in the cord?

Averell Hause

Carnegie Mellon University

Problem 52

An $85 \mathrm{~kg}$ man lowers himself to the ground from a height of $10.0 \mathrm{~m}$ by holding onto a rope that runs over a frictionless pulley to a $65 \mathrm{~kg}$ sandbag. With what speed does the man hit the ground if he started from rest?

Averell Hause

Carnegie Mellon University

Problem 53

In Fig. $5-48$, three connected blocks are and 65 . pulled to the right on a horizontal frictionless table by a force of magnitude $T_{3}=65.0 \mathrm{~N}$. If $m_{1}=12.0 \mathrm{~kg}$, $m_{2}=24.0 \mathrm{~kg}$, and $m_{3}=31.0 \mathrm{~kg}$, calculate (a) the magnitude of the system's acceleration, (b) the tension $T_{1}$, and (c) the tension $T_{2}$.

Prabhu Ramji

Numerade Educator

Problem 54

Figure $5-49$ shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are $m_{1}=12 \mathrm{~kg}$, $m_{3}=15 \mathrm{~kg}, m_{4}=20 \mathrm{~kg}, T_{2}=111 \mathrm{~N}$, and $T_{4}=222 \mathrm{~N}$. Find the pen-
guin mass $m_{2}$ that is not given.

Prabhu Ramji

Numerade Educator

Problem 55

Two blocks are in contact on a frictionless table. A horizontal force is applied to the larger block, as shown in Fig. 5-50. (a) If $m_{1}=2.3 \mathrm{~kg}$, $m_{2}=1.2 \mathrm{~kg}$, and $F=3.2 \mathrm{~N}$, find the magnitude of the force between the two blocks. (b) Show that if a force of the same magnitude $F$ is applied to the smaller block but in the opposite direction, the magnitude of the force between the blocks is $2.1 \mathrm{~N}$, which is not the same value calculated in
(a). (c) Explain the difference.

Averell Hause

Carnegie Mellon University

Problem 56

In Fig. $5-51 a$, a constant horizontal force $\vec{F}_{a}$ is applied to block $A$, which pushes against block $B$ with a $20.0 \mathrm{~N}$ force directed horizontally to the right. In Fig. $5-51 b$, the same force $\vec{F}_{a}$ is applied to block $B$; now block $A$ pushes on block $B$ with a $10.0 \mathrm{~N}$ force directed horizontally to the left. The blocks have a combined mass of $12.0 \mathrm{~kg}$. What are the magnitudes of (a) their acceleration in Fig. $5-51 a$ and (b) force $\vec{F}_{a}$ ?

Vishal Gupta

Numerade Educator

Problem 57

A block of mass $m_{1}=3.70 \mathrm{~kg}$ on a frictionless plane inclined at angle $\theta=30.0^{\circ}$ is connected by a cord over a massless, frictionless pulley to a second block of mass $m_{2}=2.30 \mathrm{~kg}$ (Fig. 5-52). What are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord?

Prabhu Ramji

Numerade Educator

Problem 58

Figure $5-53$ shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is $95.0 \mathrm{~kg}$. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and

MS

Michael Shaikhet

Numerade Educator

Problem 59

A $10 \mathrm{~kg}$ monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a $15 \mathrm{~kg}$ package on the ground (Fig. 5-54). (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are the (b) magnitude and (c) direction of the monkey's acceleration and (d) the tension in the rope?

Averell Hause

Carnegie Mellon University

Problem 60

Figure $5-45$ shows a $5.00 \mathrm{~kg}$ block being pulled along a frictionless floor by a cord that applies_a force of constant magnitude $20.0 \mathrm{~N}$ but with an angle $\theta(t)$ that varies with time. When angle $\theta=25.0^{\circ}$, at what rate is the acceleration of the block changing if (a) $\theta(t)=$ $\left(2.00 \times 10^{-2} \mathrm{deg} / \mathrm{s}\right) t$ and $(\mathrm{b}) \theta(t)=$
The angle should be in radians.)

Prabhu Ramji

Numerade Educator

Problem 61

A hot-air balloon of mass $M$ is descending vertically with downward acceleration of magnitude $a$. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude $a$ ? Assume that the upward force from the air (the lift) does not change because of the decrease in mass.

Averell Hause

Carnegie Mellon University

Problem 62

In shot putting, many athletes elect to launch the shot at an angle that is smaller than the theoretical one (about $42^{\circ}$ ) at which the distance of a projected ball at the same speed and height is greatest. One reason has to do with the speed the athlete can give the shot during the acceleration phase of the throw. Assume that a $7.260 \mathrm{~kg}$ shot is accelerated along a straight path of length $1.650 \mathrm{~m}$ by a constant applied force of magnitude $380.0 \mathrm{~N}$, starting with an initial speed of $2.500 \mathrm{~m} / \mathrm{s}$ (due to the athlete's preliminary motion). What is the shot's speed at the end of the acceleration phase if the angle between the path and the horizontal is
(a) $30.00^{\circ}$ and (b) $42.00^{\circ}$ ? (Hint: Treat the motion as though it were along a ramp at the given angle.) (c) By what percent is the launch speed decreased if the athlete increases the angle from $30.00^{\circ}$ to $42.00^{\circ} ?$

Averell Hause

Carnegie Mellon University

Problem 63

Figure $5-55$ gives, as a function of time $t$, the force component $F_{x}$ that acts on a $3.00 \mathrm{~kg}$ ice block that can move only along the $x$ axis. At $t=0$, the block is moving in the positive direction of the axis, with a speed of $3.0 \mathrm{~m} / \mathrm{s}$. What are its (a) speed and (b) direction of travel at $t=11 \mathrm{~s}$ ?

Averell Hause

Carnegie Mellon University

Problem 64

Figure $5-56$ shows a box of mass $m_{2}=1.0 \mathrm{~kg}$ on a frictionless plane inclined at angle $\theta=30^{\circ} .$ It is connected by a cord of negligible mass to a box of mass $m_{1}=3.0 \mathrm{~kg}$ on a horizontal frictionless surface. The pulley is frictionless and massless. (a) If the magnitude of horizontal force $\vec{F}$ is $2.3 \mathrm{~N}$, what is the tension in the connecting cord? (b) What is the largest value the magnitude of $\vec{F}$ may have without the cord becoming slack?

Averell Hause

Carnegie Mellon University

Problem 65

(a) Figure $5-47$ shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time $t=0$, container 1 has mass $1.30 \mathrm{~kg}$ and container 2 has mass $2.80 \mathrm{~kg}$, but container 1 is losing mass (through a leak) at the constant rate of $0.200 \mathrm{~kg} / \mathrm{s}$ At what rate is the acceleration magnitude of the containers changing at (a) $t=0$ and (b) $t=3.00 \mathrm{~s}$ ? (c) When does the acceleration reach its maximum value?

Prabhu Ramji

Numerade Educator

Problem 66

Figure $5-57$ shows a section of a cable-car system. The maximum permissible mass of each car with occupants is $2800 \mathrm{~kg}$. The cars, riding on a support cable, are pulled by a second cable attached to the support tower on each car. Assume that the cables are taut and inclined at angle $\theta=35^{\circ} .$ What is the difference in tension between adjacent sections of pull cable if the cars are at the maximum permissible mass and are being accelerated up the incline at $0.81 \mathrm{~m} / \mathrm{s}^{2} ?$

Averell Hause

Carnegie Mellon University

Problem 67

Figure $5-58$ shows three blocks attached by cords that loop over frictionless pulleys. Block $B$ lies on a frictionless table; the masses are $m_{A}=6.00 \mathrm{~kg}, m_{B}=8.00$
$\mathrm{kg}$, and $m_{C}=10.0 \mathrm{~kg}$. When the blocks are released, what is the tension in the cord at the right?

Averell Hause

Carnegie Mellon University

Problem 68

A shot putter launches a $7.260 \mathrm{~kg}$ shot by pushing it along a straight line of length $1.650 \mathrm{~m}$ and at an angle of $34.10^{\circ}$ from the horizontal, accelerating the shot to the launch speed from its initial speed of $2.500 \mathrm{~m} / \mathrm{s}$ (which is due to the athlete's preliminary motion). The shot leaves the hand at a height of $2.110 \mathrm{~m}$ and at an angle of $34.10^{\circ}$, and it lands at a horizontal distance of $15.90 \mathrm{~m}$. What is the magnitude of the athlete's average force on the shot during the acceleration phase? (Hint: Treat the motion during the acceleration phase as though it were along a ramp at the given angle.)

Averell Hause

Carnegie Mellon University

Problem 69

In Fig. $5-59,4.0 \mathrm{~kg}$ block $A$ and $6.0 \mathrm{~kg}$ block $B$ are connected by a string of negligible mass. Force $\vec{F}_{A}=(12 \mathrm{~N}) \hat{\mathrm{i}}$ acts on block $A$; force $\vec{F}_{B}=(24 \mathrm{~N}) \hat{\mathrm{i}}$ acts on block $B .$ What is the tension in the string?

Averell Hause

Carnegie Mellon University

Problem 70

An $80 \mathrm{~kg}$ man drops to a concrete patio from a window $0.50 \mathrm{~m}$ above the patio. He neglects to bend his knees on landing, taking $2.0 \mathrm{~cm}$ to stop. (a) What is his average acceleration from when his feet first touch the patio to when he stops? (b) What is the magnitude of the average stopping force exerted on him be the ratio?

Prabhu Ramji

Numerade Educator

Problem 71

Figure $5-60$ shows a box of dirty money $\left(\operatorname{mass} m_{1}=3.0 \mathrm{~kg}\right)$ on a frictionless plane inclined at angle $\theta_{1}=30^{\circ} .$ The box is connected via a cord of negligible mass to a box of laundered money $\left(\right.$ mass $m_{2}=2.0 \mathrm{~kg}$ ) on a frictionless plane inclined at angle $\theta_{2}=60^{\circ} .$ The pulley is frictionless and has negligible mass. What is the tension in the cord?

Averell Hause

Carnegie Mellon University

Problem 72

Three forces act on a particle that moves with unchanging velocity $\vec{v}=(2 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}-(7 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}$. Two of the forces are $\vec{F}_{1}=(2 \mathrm{~N}) \hat{\mathrm{i}}+$ $(3 \mathrm{~N}) \hat{\mathrm{j}}+(-2 \mathrm{~N}) \hat{\mathrm{k}}$ and $\vec{F}_{2}=(-5 \mathrm{~N}) \hat{\mathrm{i}}+(8 \mathrm{~N}) \hat{\mathrm{j}}+(-2 \mathrm{~N}) \hat{\mathrm{k}}$. What is
the third force?

Averell Hause

Carnegie Mellon University

Problem 73

In Fig. 5-61, a tin of antioxidants $\left(m_{1}=1.0 \mathrm{~kg}\right)$ on a frictionless inclined surface is connected to a tin of corned beef $\left(m_{2}=\right.$ $2.0 \mathrm{~kg}$ ). The pulley is massless and frictionless. An upward force of magnitude $F=6.0 \mathrm{~N}$ acts on the corned beef tin, which has a downward acceleration of $5.5 \mathrm{~m} / \mathrm{s}^{2}$. What are (a) the tension in the connecting cord and (b) angle $\beta$ ?

Prabhu Ramji

Numerade Educator

Problem 74

The only two forces acting on a body have magnitudes of $20 \mathrm{~N}$ and $35 \mathrm{~N}$ and directions that differ by $80^{\circ}$. The resulting acceleration has a magnitude of $20 \mathrm{~m} / \mathrm{s}^{2}$. What is the mass of the body?

Averell Hause

Carnegie Mellon University

Problem 75

Figure $5-62$ is an overhead view of a $12 \mathrm{~kg}$ tire that is to be pulled by three horizontal ropes. One rope's force $\left(F_{1}=50 \mathrm{~N}\right)$ is indicated. The forces from the other ropes are to be oriented such that the tire's acceleration magnitude $a$ is least. What is that least $a$ if (a) $F_{2}=$ $30 \mathrm{~N}, F_{3}=20 \mathrm{~N} ;(\mathrm{b}) F_{2}=30 \mathrm{~N}, F_{3}=$
$10 \mathrm{~N} ;$ and $(\mathrm{c}) F_{2}=F_{3}=30 \mathrm{~N} ?$

Averell Hause

Carnegie Mellon University

Problem 76

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$, as shown in Fig. $5-63 .$ A horizontal force $\vec{F}$ acts on one end of the rope. (a) Show that the rope must sag, even if only by an imperceptible amount. Then, assuming that the sag is negligible, find (b) the acceleration of rope and block, (c) the force on the block from the rope, and (d) the tension in the rope at its midpoint.

Donald Albin

Numerade Educator

Problem 77

A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a force of magnitude $F=450 \mathrm{~N}$ on the rope, which is inclined at an upward angle $\theta=38^{\circ}$ to the horizontal, and the floor exerts a horizontal force of magnitude $f=125 \mathrm{~N}$ that opposes the motion. Calculate the magnitude of the acceleration of the crate if (a) its mass is $310 \mathrm{~kg}$ and $(\mathrm{b})$ its weight is $310 \mathrm{~N}$.

Averell Hause

Carnegie Mellon University

Problem 78

In Fig. 5-64, a force $\vec{F}$ of magnitude $12 \mathrm{~N}$ is applied to a FedEx box of mass $m_{2}=1.0 \mathrm{~kg}$. The force is directed up a plane tilted by $\theta=$ $37^{\circ}$. The box is connected by a cord to a UPS box of mass $m_{1}=3.0 \mathrm{~kg}$ on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. What is the tension in the cord?

Averell Hause

Carnegie Mellon University

Problem 79

A certain particle has a weight of $22 \mathrm{~N}$ at a point where $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$. What are its (a) weight and (b) mass at a point where $g=4.9 \mathrm{~m} / \mathrm{s}^{2} ?$ What are its (c) weight and (d) mass if it is moved to a point in space where $g=0$ ?

Averell Hause

Carnegie Mellon University

Problem 80

An $80 \mathrm{~kg}$ person is parachuting and experiencing a downward acceleration of $2.5 \mathrm{~m} / \mathrm{s}^{2}$. The mass of the parachute is $5.0 \mathrm{~kg}$. (a) What is the upward force on the open parachute from the air? (b) What is the downward force on the parachute from the person?

Averell Hause

Carnegie Mellon University

Problem 81

A spaceship lifts off vertically from the Moon, where $g=$ $1.6 \mathrm{~m} / \mathrm{s}^{2}$. If the ship has an upward acceleration of $1.0 \mathrm{~m} / \mathrm{s}^{2}$ as it lifts off, what is the magnitude of the force exerted by the ship on its pilot, who weighs $735 \mathrm{~N}$ on Earth?

Paul Gabriel

Numerade Educator

Problem 82

In the overhead view of Fig. 5-65, five forces pull on a box of mass $m=4.0 \mathrm{~kg}$. The force magnitudes are $F_{1}=11 \mathrm{~N}, \quad F_{2}=17 \mathrm{~N}$, $F_{3}=3.0 \mathrm{~N}, F_{4}=14 \mathrm{~N}$, and $F_{5}=5.0 \mathrm{~N}$ and angle $\theta_{4}$ is $30^{\circ}$. Find the box's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the $x$ axis.

Paul A.

California State Polytechnic University, Pomona

Problem 83

A certain force gives an object of mass $m_{1}$ an acceleration of $12.0 \mathrm{~m} / \mathrm{s}^{2}$ and an object of mass $m_{2}$ an acceleration of $3.30$ $\mathrm{m} / \mathrm{s}^{2} .$ What acceleration would the force give to an object of mass
(a) $m_{2}-m_{1}$ and
(b) $m_{2}+m_{1}$ ?

Averell Hause

Carnegie Mellon University

Problem 84

You pull a short refrigerator with a constant force $\vec{F}$ across a greased (frictionless) floor, either with $\vec{F}$ horizontal (case 1) or with $\vec{F}$ tilted upward at an angle $\theta$ (case 2). (a) What is the ratio of the refrigerator's speed in case 2 to its speed in case 1 if you pull for a certain time $t ?(\mathrm{~b})$ What is this ratio if you pull for a certain distance $d ?$

Averell Hause

Carnegie Mellon University

Problem 85

A $52 \mathrm{~kg}$ circus performer is to slide down a rope that will break if the tension exceeds $425 \mathrm{~N}$. (a) What happens if the performer hangs stationary on the rope? (b) At what magnitude of acceleration does the performer just avoid breaking the rope?

Averell Hause

Carnegie Mellon University

Problem 86

Compute the weight of a $75 \mathrm{~kg}$ space ranger (a) on Earth,
(b) on Mars, where $g=3.7 \mathrm{~m} / \mathrm{s}^{2}$, and $(\mathrm{c})$ in interplanetary space, where $g=0 .(\mathrm{d})$ What is the ranger's mass at each location?

Averell Hause

Carnegie Mellon University

Problem 87

An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads $65 \mathrm{~N}$ when the cab is standing still. What is the reading when the cab is moving upward
(a) with a constant speed of $7.6 \mathrm{~m} / \mathrm{s}$ and (b) with a speed of $7.6 \mathrm{~m} / \mathrm{s}$ while decelerating at a rate of $2.4 \mathrm{~m} / \mathrm{s}^{2}$ ?

Averell Hause

Carnegie Mellon University

Problem 88

Imagine a landing craft approaching the surface of Callisto, one of Jupiter's moons. If the engine provides an upward force (thrust) of $3260 \mathrm{~N}$, the craft descends at constant speed; if the engine provides only $2200 \mathrm{~N}$, the craft accelerates downward at $0.39 \mathrm{~m} / \mathrm{s}^{2} .$ (a) What is the weight of the landing craft in the vicinity of Callisto's surface? (b) What is the mass of the craft? (c) What is the magnitude of the free-fall acceleration near the surface of Callisto?

Averell Hause

Carnegie Mellon University

Problem 89

A $1400 \mathrm{~kg}$ jet engine is fastened to the fuselage of a passenger jet by just three bolts (this is the usual practice). Assume that each bolt supports one-third of the load. (a) Calculate the force on each bolt as the plane waits in line for clearance to take off. (b) During flight, the plane encounters turbulence, which suddenly imparts an upward vertical acceleration of $2.6 \mathrm{~m} / \mathrm{s}^{2}$ to the plane. Calculate the force on each bolt now.

Averell Hause

Carnegie Mellon University

Problem 90

An interstellar ship has a mass of $1.20 \times 10^{6} \mathrm{~kg}$ and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of $0.10 c$ (where $c$ is the speed of light, $3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ) relative to the star system in $3.0$ days? (b) What is that acceleration in $g$ units? (c) What force is required for the acceleration? (d) If the engines are shut down when $0.10 c$ is reached (the speed then remains constant), how long does the ship take (start to finish) to journey $5.0$ light-months, the distance that light travels in $5.0$ months?

Prabhu Ramji

Numerade Educator

Problem 91

A motorcycle and $60.0 \mathrm{~kg}$ rider accelerate at $3.0 \mathrm{~m} / \mathrm{s}^{2}$ up a ramp inclined $10^{\circ}$ above the horizontal. What are the magnitudes of (a) the net force on the rider and (b) the force on the rider from the motorcycle?

Averell Hause

Carnegie Mellon University

Problem 92

Compute the initial upward acceleration of a rocket of mass $1.3 \times 10^{4} \mathrm{~kg}$ if the initial upward force produced by its engine (the thrust) is $2.6 \times 10^{5} \mathrm{~N}$. Do not neglect the gravitational force on the rocket.

Averell Hause

Carnegie Mellon University

Problem 93

Figure $5-66 a$ shows a mobile hanging from a ceiling; it consists of two metal pieces $\left(m_{1}=3.5 \mathrm{~kg}\right.$ and $\left.m_{2}=4.5 \mathrm{~kg}\right)$ that are strung together by cords of negligible mass. What is the tension in
(a) the bottom cord and (b) the top cord? Figure $5-66 b$ shows a mobile consisting of three metal pieces. Two of the masses are $m_{3}=$ $4.8 \mathrm{~kg}$ and $m_{5}=5.5 \mathrm{~kg}$. The tension in the top cord is $199 \mathrm{~N}$. What is the tension in (c) the lowest cord and (d) the middle cord?

Averell Hause

Carnegie Mellon University

Problem 94

For sport, a $12 \mathrm{~kg}$ armadillo runs onto a large pond of level, frictionless ice. The armadillo's initial velocity is $5.0 \mathrm{~m} / \mathrm{s}$ along the positive direction of an $x$ axis. Take its initial position on the ice as being the origin. It slips over the ice while being pushed by a wind with a force of $17 \mathrm{~N}$ in the positive direction of the $y$ axis. In unitvector notation, what are the animal's (a) velocity and (b) position vector when it has slid for $3.0$ s?

Averell Hause

Carnegie Mellon University

Problem 95

Suppose that in Fig. 5-12, the masses of the blocks are $2.0 \mathrm{~kg}$ and $4.0 \mathrm{~kg}$. (a) Which mass should the hanging block have if the magnitude of the acceleration is to be as large as possible? What then are (b) the magnitude of the acceleration and (c) the tension in the cord?

Averell Hause

Carnegie Mellon University

Problem 96

A nucleus that captures a stray neutron must bring the neutron to a stop within the diameter of the nucleus by means of the strong force. That force, which "glues" the nucleus together, is approximately zero outside the nucleus. Suppose that a stray neutron with an initial speed of $1.4 \times 10^{7} \mathrm{~m} / \mathrm{s}$ is just barely captured by a nucleus with diameter $d=1.0 \times 10^{-14} \mathrm{~m}$. Assuming the strong force on the neutron is constant, find the magnitude of that force. The neutron's mass is $1.67 \times 10^{-27} \mathrm{~kg}$. 97 If the $1 \mathrm{~kg}$ standard body is accelerated by only $\vec{F}_{1}=$ $(3.0 \mathrm{~N}) \hat{\mathrm{i}}+(4.0 \mathrm{~N}) \hat{\mathrm{j}}$ and $\vec{F}_{2}=(-2.0 \mathrm{~N}) \hat{\mathrm{i}}+(-6.0 \mathrm{~N}) \hat{\mathrm{j}}$, then what
is $\vec{F}_{\text {net }}$ (a) in unit-vector notation and as (b) a magnitude and
(c) an angle relative to the positive $x$ direction? What are the (d) magnitude and (e) angle of $\vec{a}$ ?

Jose Carlos

Numerade Educator

Problem 97

If the $1 \mathrm{~kg}$ standard body is accelerated by only $\vec{F}_{1}=$ $(3.0 \mathrm{~N}) \hat{\mathrm{i}}+(4.0 \mathrm{~N}) \hat{\mathrm{j}}$ and $\vec{F}_{2}=(-2.0 \mathrm{~N}) \hat{\mathrm{i}}+(-6.0 \mathrm{~N}) \hat{\mathrm{j}}$, then what is $\vec{F}_{\text {net }}($ a $)$ in unit-vector notation and as (b) a magnitude and
(c) an angle relative to the positive $x$ direction? What are the (d) magnitude and (e) angle of $\vec{a}$ ?

Prabhu Ramji

Numerade Educator