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University Physics Volume 1

Samuel J. Ling, Jeff Sanny, William Moebs

Chapter 12

Static Equilibrium and Elasticity - all with Video Answers

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Chapter Questions

03:58

Problem 1

What can you say about the velocity of a moving body that is in dynamic equilibrium?

BM
Bob Mckinnon
Numerade Educator
06:42

Problem 2

Under what conditions can a rotating body be in equilibrium? Give an example.

BM
Bob Mckinnon
Numerade Educator
07:41

Problem 3

What three factors affect the torque created by a force relative to a specific pivot point?

BM
Bob Mckinnon
Numerade Educator
03:55

Problem 4

Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this help?

BM
Bob Mckinnon
Numerade Educator
01:31

Problem 5

If there is only one external force (or torque) acting on an object, it cannot be in equilibrium.

BM
Bob Mckinnon
Numerade Educator
03:44

Problem 6

If an object is in equilibrium there must be an even number of forces acting on it.

BM
Bob Mckinnon
Numerade Educator
03:03

Problem 7

If an odd number of forces act on an object, the object be in equilibrium.

BM
Bob Mckinnon
Numerade Educator
03:57

Problem 8

A body moving in a circle with a constant speed is in rotational equilibrium.

BM
Bob Mckinnon
Numerade Educator
02:03

Problem 9

What purpose is served by a long and flexible pole carried by wire-walkers?

BM
Bob Mckinnon
Numerade Educator
04:23

Problem 10

Is it possible to rest a ladder against a rough wall when the floor is frictionless?

BM
Bob Mckinnon
Numerade Educator
06:29

Problem 11

Show how a spring scale and a simple fulcrum can be used to weigh an object whose weight is larger than the maximum reading on the scale.

BM
Bob Mckinnon
Numerade Educator
03:13

Problem 12

A painter climbs a ladder. Is the ladder more likely to slip when the painter is near the bottom or near the top?

BM
Bob Mckinnon
Numerade Educator
03:42

Problem 13

Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

BM
Bob Mckinnon
Numerade Educator
02:10

Problem 14

When a glass bottle full of vinegar warms up, both the vinegar and the glass expand, but the vinegar expands significantly more with temperature than does the glass. The bottle will break if it is filled up to its very tight cap. Explain why and how a pocket of air above the vinegar prevents the bottle from breaking.

BM
Bob Mckinnon
Numerade Educator
03:52

Problem 15

A thin wire strung between two nails in the wall is used to support a large picture. Is the wire likely to snap if it is strung tightly or if it is strung so that it sags considerably?

BM
Bob Mckinnon
Numerade Educator
01:06

Problem 16

Review the relationship between stress and strain. Can you find any similarities between the two quantities?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:58

Problem 17

What type of stress are you applying when you press on the ends of a wooden rod? When you pull on its ends?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:14

Problem 18

Can compressive stress be applied to a rubber band?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:13

Problem 19

Can Young's modulus have a negative value? What about the bulk modulus?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:37

Problem 20

If a hypothetical material has a negative bulk modulus, what happens when you squeeze a piece of it?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:11

Problem 21

Discuss how you might measure the bulk modulus of a liquid.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:01

Problem 22

What is meant when a fishing line is designated as "a 10-lb test?"

Surjit Tewari
Surjit Tewari
Numerade Educator
01:40

Problem 23

Steel rods are commonly placed in concrete before it sets. What is the purpose of these rods?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:36

Problem 24

When tightening a bolt, you push perpendicularly on a wrench with a force of $165 \mathrm{N}$ at a distance of $0.140 \mathrm{m}$ from the center of the bolt. How much torque are you exerting relative to the center of the bolt?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:43

Problem 25

When opening a door, you push on it perpendicularly with a force of $55.0 \mathrm{N}$ at a distance of $0.850 \mathrm{m}$ from the hinges. What torque are you exerting relative to the hinges?

Surjit Tewari
Surjit Tewari
Numerade Educator
10:26

Problem 26

Find the magnitude of the tension in each supporting cable shown below. In each case, the weight of the suspended body is $100.0 \mathrm{N}$ and the masses of the cables are negligible.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:30

Problem 27

What force must be applied at point $P$ to keep the structure shown in equilibrium? The weight of the structure is negligible.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:58

Problem 28

Is it possible to apply a force at $P$ to keep in equilibrium the structure shown? The weight of the structure is negligible.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:08

Problem 29

Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of $17.5 \mathrm{N}$ at a distance of $0.600 \mathrm{m}$ from the hinges, and the second child pushes at a distance of $0.450 \mathrm{m}$. What force must the second child exert to keep the door from moving? Assume friction is negligible.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:07

Problem 30

A small 1000-kg SUV has a wheel base of 3.0 m. If $60 \%$ if its weight rests on the front wheels, how far behind the front wheels is the wagon's center of mass?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:57

Problem 31

The uniform seesaw is balanced at its center of mass, as seen below. The smaller boy on the right has a mass of 40.0 kg. What is the mass of his friend?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:41

Problem 32

A uniform plank rests on a level surface as shown below. The plank has a mass of $30 \mathrm{kg}$ and is $6.0 \mathrm{m}$ long. How much mass can be placed at its right end before it tips? (Hint: When the board is about to tip over, it makes contact with the surface only along the edge that becomes a momentary axis of rotation.)

Surjit Tewari
Surjit Tewari
Numerade Educator
01:19

Problem 33

The uniform seesaw shown below is balanced on a fulcrum located 3.0 $\mathrm{m}$ from the left end. The smaller boy on the right has a mass of $40 \mathrm{kg}$ and the bigger boy on the left has a mass 80 kg. What is the mass of the board?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:35

Problem 34

In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tree 15 m away, as shown below. He then pulls on the center of the rope with a force of $400 \mathrm{N},$ which causes its center to be displaced 0.30 m, as shown. What is the force of the rope on the car?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:33

Problem 35

A uniform 40.0-kg scaffold of length 6.0 m is supported by two light cables, as shown below. An 80.0-kg painter stands $1.0 \mathrm{m}$ from the left end of the scaffold, and his painting equipment is $1.5 \mathrm{m}$ from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the equipment.

Dominador Tan
Dominador Tan
Numerade Educator
03:32

Problem 36

When the structure shown below is supported at point $P,$ it is in equilibrium. Find the magnitude of force $F$ and the force applied at $P .$ The weight of the structure is negligible.

Surjit Tewari
Surjit Tewari
Numerade Educator
04:20

Problem 37

To get up on the roof, a person (mass $70.0 \mathrm{kg}$ ) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder $2.00 \mathrm{m}$ from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is $2.00 \mathrm{m}$ from the bottom. The person is standing $3.00 \mathrm{m}$ from the bottom. Find the normal reaction and friction forces on the ladder at its base.

Surjit Tewari
Surjit Tewari
Numerade Educator
03:00

Problem 38

A uniform horizontal strut weighs 400.0 N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 200.0
N. The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.

Surjit Tewari
Surjit Tewari
Numerade Educator
03:44

Problem 39

The forearm shown below is positioned at an angle $\theta$ with respect to the upper arm, and a 5.0 -kg mass is held in the hand. The total mass of the forearm and hand is 3.0 kg, and their center of mass is $15.0 \mathrm{cm}$ from the elbow.
(a) What is the magnitude of the force that the biceps muscle exerts on the forearm for $\theta=60^{\circ} ?$ (b) What is the magnitude of the force on the elbow joint for the same angle? (c) How do these forces depend on the angle $\theta$ ?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:53

Problem 40

The uniform boom shown below weighs 3000 N. It is supported by the horizontal guy wire and by the hinged support at point $A$. What are the forces on the boom due to the wire and due to the support at $A$ ? Does the force at $A$ act along the boom?

Supratim Pal
Supratim Pal
Numerade Educator
03:46

Problem 41

The uniform boom shown below weighs 700 N, and the object hanging from its right end weighs $400 \mathrm{N}$. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:59

Problem 42

A 12.0-m boom, AB, of a crane lifting a 3000-kg load is shown below. The center of mass of the boom is at its geometric center, and the mass of the boom is 1000 kg. For the position shown, calculate tension $T$ in the cable and the force at the axle $A$.

Ummatul Choudary
Ummatul Choudary
Numerade Educator
02:29

Problem 43

A uniform trapdoor shown below is 1.0 m by 1.5 m and weighs 300 N. It is supported by a single hinge (H), and by a light rope tied between the middle of the door and the floor. The door is held at the position shown, where its slab makes a $30^{\circ}$ angle with the horizontal floor and the rope makes a $20^{\circ}$ angle with the floor. Find the tension in the rope and the force at the hinge.

Anand Jangid
Anand Jangid
Numerade Educator
06:15

Problem 44

A 90-kg man walks on a sawhorse, as shown below. The sawhorse is $2.0 \mathrm{m}$ long and $1.0 \mathrm{m}$ high, and its mass is $25.0 \mathrm{kg} .$ Calculate the normal reaction force on each leg at the contact point with the floor when the man is $0.5 \mathrm{m}$ from the far end of the sawhorse. (Hint: At each end, find the total reaction force first. This reaction force is the vector sum of two reaction forces, each acting along one leg. The normal reaction force at the contact point with the floor is the normal (with respect to the floor) component of this force.)

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles
02:03

Problem 45

The "lead" in pencils is a graphite composition with
a Young's modulus of approximately $1.0 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:10

Problem 46

TV broadcast antennas are the tallest artificial structures on Earth. In $1987,$ a 72.0 -kg physicist placed himself and 400 kg of equipment at the top of a 610 -m-high antenna to perform gravity experiments. By how much was the antenna compressed, if we consider it to be equivalent to a steel cylinder $0.150 \mathrm{m}$ in radius?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:15

Problem 47

By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 $\begin{array}{llllll}\mathrm{m} & \text { below } & \mathrm{a} & \text { rock } & \text { outcropping? } & \text { (For } & \text { nylon, }\end{array}$ $\left.Y=1.35 \times 10^{9} \mathrm{Pa} .\right)$.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:14

Problem 48

When water freezes, its volume increases by 9.05\%. What force per unit area is water capable of exerting on a container when it freezes?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:00

Problem 49

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2\%. Calculate the force exerted by the juice per square centimeter if its bulk modulus is $1.8 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}, \quad$ assuming the bottle does not break.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:19

Problem 50

A disk between vertebrae in the spine is subjected to a shearing force of $600.0 \mathrm{N}$. Find its shear deformation, using the shear modulus of $1.0 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$. The disk is equivalent to a solid cylinder $0.700 \mathrm{cm}$ high and $4.00 \mathrm{cm}$ in diameter.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:46

Problem 51

A vertebra is subjected to a shearing force of 500.0 N. Find the shear deformation, taking the vertebra to be a cylinder $3.00 \mathrm{cm}$ high and $4.00 \mathrm{cm}$ in diameter. How does your result compare with the result obtained in the preceding problem? Are spinal problems more common in disks than in vertebrae?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:23

Problem 52

Calculate the force a piano tuner applies to stretch a steel piano wire by $8.00 \mathrm{mm}$, if the wire is originally 1.35 m long and its diameter is $0.850 \mathrm{mm}$.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:16

Problem 53

A 20.0-m-tall hollow aluminum flagpole is equivalent in strength to a solid cylinder $4.00 \mathrm{cm}$ in diameter. A strong wind bends the pole as much as a horizontal 900.0-N force on the top would do. How far to the side does the top of the pole flex?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:24

Problem 54

A copper wire of diameter 1.0 cm stretches 1.0\% when it is used to lift a load upward with an acceleration of $2.0 \mathrm{m} / \mathrm{s}^{2} .$ What is the weight of the load?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:30

Problem 55

As an oil well is drilled, each new section of drill pipe supports its own weight and the weight of the pipe and the drill bit beneath it. Calculate the stretch in a new 6.00-m-long steel pipe that supports a 100 -kg drill bit and a 3.00-km length of pipe with a linear mass density of 20.0 $\mathrm{kg} / \mathrm{m} .$ Treat the pipe as a solid cylinder with a $5.00-\mathrm{cm}$ diameter.

Surjit Tewari
Surjit Tewari
Numerade Educator
02:25

Problem 56

A large uniform cylindrical steel rod of density $\rho=7.8 \mathrm{g} / \mathrm{cm}^{3}$ is $2.0 \mathrm{m}$ long and has a diameter of $5.0 \mathrm{cm}$
The rod is fastened to a concrete floor with its long axis vertical. What is the normal stress in the rod at the crosssection located at (a) $1.0 \mathrm{m}$ from its lower end? (b) $1.5 \mathrm{m}$ from the lower end?

Ajay Singhal
Ajay Singhal
Numerade Educator
01:07

Problem 57

A 90-kg mountain climber hangs from a nylon rope and stretches it by $25.0 \mathrm{cm} .$ If the rope was originally 30.0 m long and its diameter is $1.0 \mathrm{cm},$ what is Young's modulus for the nylon?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:11

Problem 58

A suspender rod of a suspension bridge is $25.0 \mathrm{m}$ long. If the rod is made of steel, what must its diameter be so that it does not stretch more than $1.0 \mathrm{cm}$ when a $2.5 \times 10^{4}-\mathrm{kg}$ truck passes by it? Assume that the rod supports all of the weight of the truck.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:16

Problem 59

A copper wire is $1.0 \mathrm{m}$ long and its diameter is 1.0 mm. If the wire hangs vertically, how much weight must be added to its free end in order to stretch it $3.0 \mathrm{mm}$ ?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:50

Problem 60

A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second $100-\mathrm{N}$ weight is added to the wire, it stretches $3.0 \mathrm{mm}$. The diameter and the length of the wire are $1.0 \mathrm{mm}$ and $2.0 \mathrm{m}$, respectively. What is Young's modulus of the metal used to manufacture the wire?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:08

Problem 61

61. The bulk modulus of a material is $1.0 \times 10^{11} \mathrm{N} / \mathrm{m}^{2}$ What fractional change in volume does a piece of this material undergo when it is subjected to a bulk stress increase of $10^{7} \mathrm{N} / \mathrm{m}^{2}$ ? Assume that the force is applied uniformly over the surface.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:54

Problem 62

Normal forces of magnitude $1.0 \times 10^{6} \mathrm{N}$ are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from $50.000 \mathrm{cm}$ to $49.995 \mathrm{cm} .$ What is the bulk modulus of the liquid?

Surjit Tewari
Surjit Tewari
Numerade Educator
00:56

Problem 63

During a walk on a rope, a tightrope walker creates a tension of $3.94 \times 10^{3} N$ in a wire that is stretched between two supporting poles that are $15.0 \mathrm{m}$ apart. The wire has a diameter of $0.50 \mathrm{cm}$ when it is not stretched. When the walker is on the wire in the middle between the poles the wire makes an angle of $5.0^{\circ}$ below the horizontal. How much does this tension stretch the steel wire when the walker is this position?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:05

Problem 64

When using a pencil eraser, you exert a vertical force of $6.00 \mathrm{N}$ at a distance of $2.00 \mathrm{cm}$ from the hardwooderaser joint. The pencil is $6.00 \mathrm{mm}$ in diameter and is held at an angle of $20.0^{\circ}$ to the horizontal. (a) By how much does the wood flex perpendicular to its length? (b) How much is it compressed lengthwise?

Averell Hause
Averell Hause
Carnegie Mellon University
02:05

Problem 64

When using a pencil eraser, you exert a vertical force of $6.00 \mathrm{N}$ at a distance of $2.00 \mathrm{cm}$ from the hardwooderaser joint. The pencil is $6.00 \mathrm{mm}$ in diameter and is held at an angle of $20.0^{\circ}$ to the horizontal. (a) By how much does the wood flex perpendicular to its length? (b) How much is it compressed lengthwise?

Averell Hause
Averell Hause
Carnegie Mellon University
03:27

Problem 65

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is $20.0 \mathrm{cm}$. If the pressure on the surface is increased by $200 \mathrm{MPa}$, by how much does the radius of the sphere decrease?

Surjit Tewari
Surjit Tewari
Numerade Educator
05:23

Problem 66

A uniform rope of cross-sectional area $0.50 \mathrm{cm}^{2}$ breaks when the tensile stress in it reaches $6.00 \times 10^{6} \mathrm{N} / \mathrm{m}^{2}$. (a) What is the maximum load that can be lifted slowly at a constant speed by the rope? (b) What is the maximum load that can be lifted by the rope with an acceleration of $4.00 \mathrm{m} / \mathrm{s}^{2} ?$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:20

Problem 67

One end of a vertical metallic wire of length $2.0 \mathrm{m}$ and diameter $1.0 \mathrm{mm}$ is attached to a ceiling, and the other end is attached to a $5.0-\mathrm{N}$ weight pan, as shown below. The position of the pointer before the pan is $4.000 \mathrm{cm} .$ Different weights are then added to the pan area, and the position of the pointer is recorded in the table shown. Plot stress versus strain for this wire, then use the resulting curve to determine Young's modulus and the proportionality limit of the metal. What metal is this most likely to be?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:20

Problem 67

One end of a vertical metallic wire of length $2.0 \mathrm{m}$ and diameter $1.0 \mathrm{mm}$ is attached to a ceiling, and the other end is attached to a 5.0 - $\mathrm{N}$ weight pan, as shown below. The position of the pointer before the pan is $4.000 \mathrm{cm} .$ Different weights are then added to the pan area, and the position of the pointer is recorded in the table shown. Plot stress versus strain for this wire, then use the resulting curve to determine Young's modulus and the proportionality limit of the metal. What metal is this most likely to be?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:24

Problem 68

An aluminum $\left(\rho=2.7 \mathrm{g} / \mathrm{cm}^{3}\right)$ wire is suspended
from the ceiling and hangs vertically. How long must the wire be before the stress at its upper end reaches the proportionality limit, which is $8.0 \times 10^{7} \mathrm{N} / \mathrm{m}^{2} ?$

Surjit Tewari
Surjit Tewari
Numerade Educator
01:49

Problem 69

The coefficient of static friction between the rubber eraser of the pencil and the tabletop is $\mu_{s}=0.80 .$ If the force $\overrightarrow{\mathbf{F}}$ is applied along the axis of the pencil, as shown below, what is the minimum angle at which the pencil can stand without slipping? Ignore the weight of the pencil.

Surjit Tewari
Surjit Tewari
Numerade Educator
03:31

Problem 70

A pencil rests against a corner, as shown below. The sharpened end of the pencil touches a smooth vertical surface and the eraser end touches a rough horizontal floor. The coefficient of static friction between the eraser and the floor is $\mu_{s}=0.80 .$ The center of mass of the pencil is located $9.0 \mathrm{cm}$ from the tip of the eraser and $11.0 \mathrm{cm}$ from the tip of the pencil lead. Find the minimum angle $\theta$ for which the pencil does not slip.

Surjit Tewari
Surjit Tewari
Numerade Educator
04:58

Problem 71

A uniform 4.0-m plank weighing 200.0 N rests against the corner of a wall, as shown below. There is no friction at the point where the plank meets the corner. (a) Find the forces that the corner and the floor exert on the plank. (b) What is the minimum coefficient of static friction between

Surjit Tewari
Surjit Tewari
Numerade Educator
02:07

Problem 72

A 40-kg boy jumps from a height of 3.0 m, lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is $3.0 \mathrm{cm}^{2},$ what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than $1.7 \times 10^{8} \mathrm{Pa}$. Is the boy in danger of breaking his leg?

Surjit Tewari
Surjit Tewari
Numerade Educator
03:55

Problem 73

Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod is $2.0 \mathrm{m}$ long and has cross-sectional area $9.1 \mathrm{mm}^{2}$. If a $10,000-\mathrm{N}$ tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.

Surjit Tewari
Surjit Tewari
Numerade Educator
01:28

Problem 74

Two rods, one made of copper and the other of steel, have the same dimensions. If the copper rod stretches by $0.15 \mathrm{mm}$ under some stress, how much does the steel rod stretch under the same stress?

Surjit Tewari
Surjit Tewari
Numerade Educator
01:12

Problem 75

A horizontal force $\overrightarrow{\mathbf{F}}$ is applied to a uniform sphere in direction exact toward the center of the sphere, as shown below. Find the magnitude of this force so that the sphere remains in static equilibrium. What is the frictional force of the incline on the sphere?

Surjit Tewari
Surjit Tewari
Numerade Educator
10:07

Problem 76

When a motor is set on a pivoted mount seen below, its weight can be used to maintain tension in the drive belt. When the motor is not running the tensions $T_{1}$ and $T_{2}$ are
equal. The total mass of the platform and the motor is 100.0 $\mathrm{kg},$ and the diameter of the drive belt pulley is $16.0 \mathrm{cm}$ when the motor is off, find: (a) the tension in the belt, and (b) the force at the hinged platform support at point $C$ Assume that the center of mass of the motor plus platform is at the center of the motor.

Surjit Tewari
Surjit Tewari
Numerade Educator
08:43

Problem 77

Two wheels $A$ and $B$ with weights $w$ and $2 w$ respectively, are connected by a uniform rod with weight w/2, as shown below. The wheels are free to roll on the sloped surfaces. Determine the angle that the rod forms with the horizontal when the system is in equilibrium. Hint: There are five forces acting on the rod, which is two weights of the wheels, two normal reaction forces at points where the wheels make contacts with the wedge, and the weight of the rod.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:39

Problem 78

Weights are gradually added to a pan until a wheel of mass $M$ and radius $R$ is pulled over an obstacle of height $d$ as shown below. What is the minimum mass of the weights plus the pan needed to accomplish this?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:24

Problem 79

In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance $l_{2}$ from the end, as shown below. The weight of the shovel is $m \vec{g}$ and acts at the point of application of $\vec{F}_{2 \cdot}$ Calculate the magnitudes of the forces $\vec{F}_{1}$ and $\vec{F}_{2}$ as functions of $l_{1}, \quad l_{2}, \quad m g,$ and the weight $W$ of the load. Why do your answers not depend on the angle $\theta$ that the shovel makes with the horizontal?

Surjit Tewari
Surjit Tewari
Numerade Educator
05:24

Problem 80

A uniform rod of length $2 R$ and mass $M$ is attached to a small collar $C$ and rests on a cylindrical surface of radius R, as shown below. If the collar can slide without friction along the vertical guide, find the angle $\theta$ for which the rod is in static equilibrium.

Surjit Tewari
Surjit Tewari
Numerade Educator
08:17

Problem 81

The pole shown below is at a $90.0^{\circ}$ bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is $4.00 \times 10^{4} \mathrm{N}, \quad$ at the angles shown. The pole is 15.0
m tall, has an $18.0 \mathrm{cm}$ diameter, and can be considered to have half the strength of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of $30.0^{\circ}$ with the vertical. The guy wire is in the opposite direction of the bend.

Mayukh Banik
Mayukh Banik
Numerade Educator