College Physics: Reasoning and Relationships

Nicholas J. Giordano

Chapter 4

Forces and Motion in Two and Three Dimensions - all with Video Answers

Educators

Section 1

Statics

Problem 1

Two ropes are attached to a skater as sketched in Figure $\mathrm{P} 4.1$ and exert forces on her as shown. Find the magnitude and direction of the total force exerted by the ropes on the skater.

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 2

The three forces shown in Figure $\mathrm{P} 4.2$ act on a particle. If the particle is in translational equilibrium, find $F_{3}$ (the magnitude of force 3 ) and the angle $\theta_{3}$.

Hast Aggarwal

Numerade Educator

Problem 3

Several forces act on a particle as shown in Figure $\mathrm{P} 4.3 .$ If the particle is in translational equilibrium, what are the values of $F_{3}$ (the magnitude of force 3 ) and $\theta_{3}$ (the angle that force 3 makes with the $x$ axis)?

Hast Aggarwal

Numerade Educator

Problem 4

A man is lazily floating on an air mattress in a swimming pool (Fig. P4.4).
a. Draw a free-body diagram for the man and for the mattress.
b. Identify the reaction forces for all the forces in your free-body diagrams in part (a).
c. If the mass of the man is $110 \mathrm{kg}$ and the mass of the mattress is $2.5 \mathrm{kg},$ what is the upward force of the water on the mattress?
What is the force that the man exerts on the mattress? Note: Keep three significant figures in your
answer.

Hast Aggarwal

Numerade Educator

Problem 5

A person leans against a wall (Fig. $\mathrm{P} 4.5$ ). Draw a free-body diagram for the person. Assume there is no frictional force between the wall and the person.

Hast Aggarwal

Numerade Educator

Problem 6

The sled in Figure 4.2 is stuck in the snow. A child pulls on the rope and finds that the sled just barely begins to move when he pulls with a force of $25 \mathrm{N}$, with the rope at an angle of $30^{\circ}$ with respect to the horizontal.
a. Sketch the sled and all the forces acting on it. Also choose a coordinate system.
b. Determine the components of all the forces on the sled along the coordinate axes.
c. Write the conditions for static equilibrium along your two coordinate directions.
d. If the sled has a mass of $12 \mathrm{kg}$, what is the coefficient of friction between the sled and the snow?
e. Is this the coefficient of static friction or the coefficient of kinetic friction?
f. If the child continues to pull on the sled and it has an acceleration of $0.30 \mathrm{m} / \mathrm{s}^{2}$, find the coefficient of kinetic friction between the sled and the snow.

Hast Aggarwal

Numerade Educator

Problem 7

A system of cables is used to support a crate of mass $m=45 \mathrm{kg}$ as shown in Figure $\mathrm{P} 4.7 .$ Find the tensions in all three cables.

Vishal Gupta

Numerade Educator

Problem 8

The tightrope walker in Figure $\mathrm{P} 4.8$ gets tired and decides to stop for a rest. During this rest period, she is in translational equilibrium. She stops at middle of the rope and finds that both sides of the rope make an angle $\theta=15^{\circ}$ with the horizontal. a. Sketch the walker and the rope. Show all the forces acting on the point of the rope on which the walker stands (call this point $P$ ). Also include a coordinate system.
b. Determine the components of all the forces on point $P$ along the coordinate axes.
c. Write the conditions for static equilibrium along your two coordinate directions.
d. If the mass of the tightrope walker is $60 \mathrm{kg},$ what is the tension in the rope?

Hast Aggarwal

Numerade Educator

Problem 9

A flag of mass $2.5 \mathrm{kg}$ is supported by a single rope as shown in Figure $\mathrm{P} 4.9 .$ A strong horizontal wind exerts a force of $12 \mathrm{N}$ on the flag. Find the tension in the rope and the angle $\theta$ the rope makes with the horizontal.

Hast Aggarwal

Numerade Educator

Problem 10

A car of mass $1400 \mathrm{kg}$ is parked on a very slippery hillside (Fig. P4.10). To keep it from sliding down the hill, the owner attaches a cable. a. Sketch all the forces on the car. Include coordinate axes in your sketch.
b. Determine the components of all the forces on the car along the coordinate axes.
c. Write the conditions for static equilibrium along your two coordinate directions.
d. If there is no frictional force between the road and the tires, what is the tension in the cable?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 11

A crate is placed on an inclined board as shown in Figure $\mathrm{P} 4.11 .$ One end of the board is hinged so that the angle $\theta$ is adjustable. If the coefficient of static friction between the crate and the board is $\mu_{S}=0.30,$ what is the value of $\theta$ at which the crate just begins to slip?

Hast Aggarwal

Numerade Educator

Problem 12

Two blocks of mass $m_{1}=45 \mathrm{kg}$ and $m_{2}=12 \mathrm{kg}$ are connected by a massless string that passes over a pulley as shown in Figure $\mathrm{P} 4.12 .$ The coefficient of static friction between $m_{1}$ and the table is $\mu_{S}=0.45$ a. Will this system be in static equilibrium? Assume the pulley is frictionless.
b. Find the tension in the string.

Hast Aggarwal

Numerade Educator

Problem 13

For the system in Problem 12 and Eigure $\mathrm{P} 4.12$, how large can $m_{2}$ be made without the system starting into motion?

Hast Aggarwal

Numerade Educator

Problem 14

A rock climber of mass $60 \mathrm{kg}$ wants to make her way up the crack between two rocks as shown in Figure $\mathrm{P} 4.14 .$ The coefficient of friction between her shoes and the rock surface is $\mu_{S}=0.90 .$ What is the smallest normal force she can apply to both surfaces without slipping? Assume the rock walls are vertical. Hint: Why is the normal force between the climber and the rock on the left equal to the normal force between her and the rock on the right?

Hast Aggarwal

Numerade Educator