Engineering Mechanics: Statics SI Edition

Russell C. Hibbeler

Chapter 3

Equilibrium of a Particle - all with Video Answers

Educators

Chapter Questions

Problem 1

Determine the magnitude and direction $\theta$ of $\mathbf{F}$ so that the particle is in equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 2

The members of a truss are pin connected at joint $O$. Determine the magnitudes of $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ for equilibrium. Set $\theta=60^{\circ} .$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

The members of a truss are pin connected at joint $O$. Determine the magnitude of $\mathbf{F}_{1}$ and its angle $\theta$ for equilibrium. Set $F_{2}=6 \mathrm{kN}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 4

The members of a truss are connected to the gusset plate. If the forces are concurrent at point $O$, determine the magnitudes of $\mathbf{F}$ and $\mathbf{T}$ for equilibrium. Take $\theta=90^{\circ}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 5

The gusset plate is subjected to the forces of three members. Determine the tension force in member $C$ and its angle $\theta$ for equilibrium. The forces are concurrent at point $O$. Take $F=8 \mathrm{kN}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 6

The bearing consists of rollers, symmetrically confined within the housing. The bottom one is subjected to a $125-\mathrm{N}$ force at its contact $A$ due to the load on the shaft. Determine the normal reactions $N_{B}$ and $N_{C}$ on the bearing at its contact points $B$ and $C$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 7

Determine the tension developed in wires $C A$ and $C B$ required for equilibrium of the $10-\mathrm{kg}$ cylinder. Take $\theta=40^{\circ} .$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 8

If cable is subjected to a tension that is twice that of cable $C A,$ determine the angle $\theta$ for equilibrium of the $10-\mathrm{kg}$ cylinder. Also, what are the tensions in wires $C A$ and $C B ?$

Henry York

Numerade Educator

Problem 9

Determine the force in each cable and the force $\mathbf{F}$ needed to hold the $4-\mathrm{kg}$ lamp in the position shown. Hint:
First analyze the equilibrium at $B ;$ then, using the result for the force in $B C$, analyze the equilibrium at $C$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 10

The towing pendant $A B$ is subjected to the force of $50 \mathrm{kN}$ exerted by a tugboat. Determine the force in each of the bridles, $B C$ and $B D$, if the ship is moving forward with constant velocity.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 11

Two spheres $A$ and $B$ have an equal mass and are electrostatically charged such that the repulsive force acting between them has a magnitude of $20 \mathrm{mN}$ and is directed along line $A B$. Determine the angle $\theta$, the tension in cords $A C$ and $B C,$ and the mass $m$ of each sphere.

Mihajlo Grcic

Numerade Educator

Problem 12

Determine the stretch in each spring for equilibrium of the $2-\mathrm{kg}$ block. The springs are shown in the equilibrium position.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 13

The unstretched length of spring $A B$ is $3 \mathrm{~m}$. If the block is held in the equilibrium position shown, determine the mass of the block at $D$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 14

Determine the mass of each of the two cylinders if they cause a sag of $s=0.5 \mathrm{~m}$ when suspended from the rings at $A$ and $B$. Note that $s=0$ when the cylinders are removed.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

Determine the magnitude and direction $\theta$ of the equlibrium force $F_{A B}$ exerted along link $A B$ by the tractive apparatus shown. The suspended mass is $10 \mathrm{~kg}$. Neglect the size of the pulley at $A$.

Alexander Allen

Alexander Allen

Numerade Educator

Problem 16

The lift sling is used to hoist a container having a mass of $500 \mathrm{~kg} .$ Determine the force in each of the cables $A B$ and $A C$ as a function of $\theta .$ If the maximum tension allowed in each cable is $5 \mathrm{kN},$ determine the shortest length of cables $A B$ and $A C$ that can be used for the lift. The center of gravity of the container is located at $G$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

The springs $B A$ and $B C$ each have a stiffness of $500 \mathrm{~N} / \mathrm{m}$ and an unstretched length of $3 \mathrm{~m}$. Determine the horizontal force $\mathbf{F}$ applied to the cord which is attached to the small ring $B$ so that the displacement of $A B$ from the wall is $d=1.5 \mathrm{~m}$.

Jonah Han

Numerade Educator

Problem 18

The springs $B A$ and $B C$ each have a stiffness of $500 \mathrm{~N} / \mathrm{m}$ and an unstretched length of $3 \mathrm{~m}$. Determine the displacement $d$ of the cord from the wall when a force $F=175 \mathrm{~N}$ is applied to the cord.

Jonah Han

Numerade Educator

Problem 19

Determine the tension developed in each wire used to support the $50-\mathrm{kg}$ chandelier.

Keshav Singh

Numerade Educator

Problem 20

If the tension developed in each of the four wires is not allowed to exceed $600 \mathrm{~N},$ determine the maximum mass of the chandelier that can be supported.

Keshav Singh

Numerade Educator

Problem 21

If the spring $D B$ has an unstretched length of $2 \mathrm{~m}$, determine the stiffness of the spring to hold the $40-\mathrm{kg}$ crate in the position shown.

Rashmi Sinha

Numerade Educator

Problem 22

Determine the unstretched length of $D B$ to hold the $40-\mathrm{kg}$ crate in the position shown. Take $k=180 \mathrm{~N} / \mathrm{m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 23

Determine the stiffness $k_{T}$ of the single spring such that the force $\mathbf{F}$ will stretch it by the same amount $s$ as the force $\mathbf{F}$ stretches the two springs. Express $k_{T}$ in terms of stiffness $k_{1}$ and $k_{2}$ of the two springs.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

$ A $4-\mathrm{kg}$ sphere rests on the smooth parabolic surface. Determine the normal force it exerts on the surface and the mass $m_{B}$ of block $B$ needed to hold it in the equilibrium position shown.

Sheh Lit Chang

University of Washington

Problem 25

Cable $A B C$ has a length of $5 \mathrm{~m}$. Determine the position $x$ and the tension developed in $A B C$ required for equilibrium of the $100-\mathrm{kg}$ sack. Neglect the size of the pulley at $B$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 26

The device shown is used to straighten the frames of wrecked autos. Determine the tension of each segment of the chain, i.e., $A B$ and $B C$, if the force which the hydraulic cylinder $D B$ exerts on point $B$ is $3.50 \mathrm{kN}$, as shown.

Ryan Pollard

Numerade Educator

Problem 27

Determine the force in each cord for equilibrium of the $200-\mathrm{kg}$ crate. Cord $B C$ remains horizontal due to the roller at $C,$ and $A B$ has a length of $1.5 \mathrm{~m}$. Set $y=0.75 \mathrm{~m}$.

Ahmed Kamel

Numerade Educator

Problem 28

If the 1.5 -m-long cord $A B$ can withstand a maximum force of $3500 \mathrm{~N},$ determine the force in $\operatorname{cord} B C$ and the distance $y$ so that the $200-\mathrm{kg}$ crate can be supported.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 29

Blocks $D$ and $E$ have a mass of $4 \mathrm{~kg}$ and $6 \mathrm{~kg}$, respectively. If $x=2 \mathrm{~m}$ determine the force $\mathbf{F}$ and the sag $s$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 30

Blocks $D$ and $E$ have a mass of $4 \mathrm{~kg}$ and $6 \mathrm{~kg}$, respectively. If $F=80 \mathrm{~N},$ determine the sag $s$ and distance $x$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 31

Determine the tension developed in each cord required for equilibrium of the $20-\mathrm{kg}$ lamp.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

Determine the maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding $400 \mathrm{~N}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 33

A scale is constructed using the $10-\mathrm{kg}$ mass, the $2-\mathrm{kg}$ pan $P$, and the pulley and cord arrangement. Cord $B C A$ is $2 \mathrm{~m}$ long. If $s=0.75 \mathrm{~m}$, determine the mass $D$ in the pan. Neglect the size of the pulley.

Anand Jangid

Numerade Educator

Problem 34

The $30-\mathrm{kg}$ pipe is supported at $A$ by a system of five cords. Determine the force in each cord for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 35

Each cord can sustain a maximum tension of $500 \mathrm{~N}$. Determine the largest mass of pipe that can be supported.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 36

Determine the distances $x$ and $y$ for equilibrium if $F_{1}=800 \mathrm{~N}$ and $F_{2}=1000 \mathrm{~N}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 37

Determine the magnitude of $F_{1}$ and the distance $y$ if $x=1.5 \mathrm{~m}$ and $F_{2}=1000 \mathrm{~N}$.

Supratim Pal

Numerade Educator

Problem 38

Determine the force in cables $A B$ and $A C$ necessary to support the $12-\mathrm{kg}$ traffic light.

Jose Carlos

Numerade Educator

Problem 39

The pail and its contents have a mass of $60 \mathrm{~kg}$. If the cable is $15 \mathrm{~m}$ long, determine the distance $y$ of the pulley for equilibrium. Neglect the size of the pulley at $A$.

Vipender Yadav

Numerade Educator

Problem 40

Determine the forces in cables $A C$ and $A B$ needed to hold the $20-\mathrm{kg}$ ball $D$ in equilibrium. Take $F=300 \mathrm{~N}$ and $d=1 \mathrm{~m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

The ball $D$ has a mass of $20 \mathrm{~kg}$. If a force of $F=100 \mathrm{~N}$ is applied horizontally to the ring at $A$, determine the dimension $d$ so that the force in cable $A C$ is zero.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 42

The load has a mass of $15 \mathrm{~kg}$ and is lifted by the pulley system shown. Determine the force $\mathbf{F}$ in the cord as a function of the angle $\theta$. Plot the function of force $F$ versus the angle $\theta$ for $0 \leq \theta \leq 90^{\circ}$.

Stephen Zaffke

Numerade Educator

Problem 43

The three cables are used to support the $40-\mathrm{kg}$ flowerpot. Determine the force developed in each cable for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 44

Determine the magnitudes of $\mathbf{F}_{1}, \mathbf{F}_{2}$, and $\mathbf{F}_{3}$ for equilibrium of the particle.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 45

Determine the tension in the cables in order to support the $100-\mathrm{kg}$ crate in the equilibrium position shown.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 46

Determine the maximum mass of the crate so that the tension developed in any cable does not exceeded $3 \mathrm{kN}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 47

Determine the force in each cable needed to support the $20-\mathrm{kg}$ flowerpot.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

The lamp has a mass of $15 \mathrm{~kg}$ and is supported by a pole $A O$ and cables $A B$ and $A C$. If the force in the pole acts along its axis, determine the forces in $A O, A B,$ and $A C$ for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 49

Cables $A B$ and $A C$ can sustain a maximum tension of $500 \mathrm{~N}$, and the pole can support a maximum compression of $300 \mathrm{~N}$. Determine the maximum weight of the lamp that can be supported in the position shown. The force in the pole acts along the axis of the pole.

Keshav Singh

Numerade Educator

Problem 50

If the balloon is subjected to a net uplift force of $F=800 \mathrm{~N},$ determine the tension developed in ropes $A B, A C, A D .$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 51

If each one of the ropes will break when it is subjected to a tensile force of $450 \mathrm{~N},$ determine the maximum uplift force $\mathbf{F}$ the balloon can have before one of the ropes breaks.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 52

The shear leg derrick is used to haul the $200-\mathrm{kg}$ net of fish onto the dock. Determine the compressive force along each of the legs $A B$ and $C B$ and the tension in the winch cable $D B$. Assume the force in each leg acts along its axis.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 53

Determine the stretch in each of the two springs required to hold the $20-\mathrm{kg}$ crate in the equilibrium position shown. Each spring has an unstretched length of $2 \mathrm{~m}$ and a stiffness of $k=300 \mathrm{~N} / \mathrm{m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 54

The thin ring can be adjusted vertically between three equally long cables from which the $100-\mathrm{kg}$ chandelier is suspended. If the ring remains in the horizontal plane and $z=600 \mathrm{~mm},$ determine the tension in each cable.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 55

The thin ring can be adjusted vertically between three equally long cables from which the $100-\mathrm{kg}$ chandelier is suspended. If the ring remains in the horizontal plane and the tension in each cable is not allowed to exceed $1 \mathrm{kN},$ determine the smallest allowable distance $z$ required for equilibrium.

Narayan Hari

Numerade Educator

Problem 56

Determine the tension in each cable for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 57

The $25-\mathrm{kg}$ flowerpot is supported at $A$ by the three cords. Determine the force acting in each cord for equilibrium.

Rashmi Sinha

Numerade Educator

Problem 58

If each cord can sustain a maximum tension of $50 \mathrm{~N}$ before it fails, determine the greatest weight of the flowerpot the cords can support.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

If the mass of the flowerpot is $50 \mathrm{~kg}$, determine the tension developed in each wire for equilibrium. Set $x=1.5 \mathrm{~m}$ and $z=2 \mathrm{~m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

If the mass of the flowerpot is $50 \mathrm{~kg}$, determine the tension developed in each wire for equilibrium. Set $x=2 \mathrm{~m}$ and $z=1.5 \mathrm{~m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 61

Determine the tension developed in the three cables required to support the traffic light, which has a mass of $15 \mathrm{~kg}$. Take $h=4 \mathrm{~m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 62

Determine the tension developed in the three cables required to support the traffic light, which has a mass of $20 \mathrm{~kg}$. Take $h=3.5 \mathrm{~m}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 63

The crate has a mass of $130 \mathrm{~kg} .$ Determine the tension developed in each cable for equilibrium.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 64

If the maximum force in each rod can not exceed $1500 \mathrm{~N},$ determine the greatest mass of the crate that can be supported.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 65

Determine the force in each cable needed to support the $17.5-\mathrm{kN}(\approx 1750-\mathrm{kg})$ platform. Set $d=1.2 \mathrm{~m}$.

Keshav Singh

Numerade Educator

Problem 66

The ends of the three cables are attached to a ring at $A$ and to the edge of the uniform plate. Determine the largest mass the plate can have if each cable can support a maximum tension of $15 \mathrm{kN}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 67

A small peg $P$ rests on a spring that is contained inside the smooth pipe. When the spring is compressed so that $s=0.15 \mathrm{~m}$, the spring exerts an upward force of $60 \mathrm{~N}$ on the peg. Determine the point of attachment $A(x, y, 0)$ of cord $P A$ so that the tension in cords $P B$ and $P C$ equals $30 \mathrm{~N}$ and $50 \mathrm{~N}$, respectively.

Jonah Han

Numerade Educator

Problem 68

Determine the height $d$ of cable $A B$ so that the force in cables $A D$ and $A C$ is one-half as great as the force in cable $A B$. What is the force in each cable for this case? The flower pot has a mass of $50 \mathrm{~kg}$.

Keshav Singh

Numerade Educator