Problem 1
Figure 4.42 represents a racetrack with semicircular sections connected by straight sections. Each section has length d, and markers along the track are spaced d/4 apart. Two people drive cars counterclockwise around the track, as shown. Car X goes around the curves at constant speed vc, increases speed at constant acceleration for half of each straight section to reach a maximum speed of 2vc, then brakes at constant acceleration for the other half of each straight section to return to speed vc. Car Y also goes around the curves at constant speed vc, increases its speed at constant acceleration for one-fourth of each straight section to reach the same maximum speed 2vc, stays at that speed for half of each straight section, then brakes at constant acceleration for the remaining fourth of each straight section to return to speed vc.
(a) On the figures below, draw an arrow showing the direction of the net force on each of the cars at the positions noted by the dots. If the net force is zero at any position, label the dot with 0. Description of Figure 4.43:
(b) i. Indicate which car, if either, completes one trip around the track in less time, and justify your answer qualitatively without using equations.
ii. Justify your answer about which car, if either, completes one trip around the track in less time quantitatively with appropriate equations.
A hawk accelerates as it glides in the air. Does the force causing the acceleration come from the hawk itself? Explain.
What object or objects commonly exert forces on the following objects in motion? (a) a soccer ball being kicked, (b) a dolphin jumping, (c) a parachutist drifting to Earth.
Which of the following is true?
Earth exerts a force due to gravity on your body, and
your body exerts a smaller force on the Earth, because
your mass is smaller than the mass of the Earth.
The Moon orbits the Earth because the Earth exerts a
force on the Moon and the Moon exerts a force equal in
magnitude and direction on the Earth.
A rocket taking off exerts a force on the Earth equal to
the force the Earth exerts on the rocket.
An airplane cruising at a constant speed is not affected
by gravity.
A parachutist’s fall to Earth is determined by two opposing forces. A gravitational force of 539 N acts on the parachutist. After 2 s, she opens her parachute and experiences an air resistance of 615 N. At what speed is the parachutist falling after 10 s?
A landscaper is easing a wheelbarrow full of soil down a hill. Define the system you would analyze and list all the forces that you would need to include to calculate the acceleration of the wheelbarrow.
A figure skater has a mass of 40 kg and her partner's mass is 50 kg. She pushes against the ice with a force of 120 N, causing her and her partner to move forward. Calculate the pair’s acceleration. Assume that all forces opposing the motion, such as friction and air resistance, total 5.0 N.
Two teams are engaging in a tug–of-war. The rope suddenly snaps. Which statement is true about the forces involved?
The forces exerted by the two teams are no longer equal; the teams will accelerate in opposite directions as a result.
The forces exerted by the players are no longer balanced by the force of tension in the rope; the teams will accelerate in opposite directions as a result.
The force of gravity balances the forces exerted by the players; the teams will fall as a result
The force of tension in the rope is transferred to the players; the teams will accelerate in opposite directions as a result.
A toboggan with two riders has a total mass of 85.0 kg. A third person is pushing the toboggan with a force of 42.5 N at the top of a hill with an angle of 15°. The force of friction on the toboggan is 31.0 N. Which statement describes an accurate free-body diagram to represent the situation?
An arrow of magnitude 10.5 N points down the slope of the hill.
An arrow of magnitude 833 N points straight down.
An arrow of magnitude 833 N points perpendicular to the slope of the hill.
An arrow of magnitude 73.5 N points down the slope of the hill.
Which statement is true about drawing free-body diagrams?
Drawing a free-body diagram should be the last step in solving a problem about forces.
Drawing a free-body diagram helps you compare forces quantitatively.
The forces in a free-body diagram should always balance.
Drawing a free-body diagram can help you determine the net force.
electromagnetic attraction
electromagnetic repulsion
gravitational attraction
gravitational repulsion
gravity; attraction
electromagnetic; attraction
weak and strong nuclear; attraction
weak and strong nuclear; repulsion
a person jumping on a trampoline
a rocket blasting off from Earth
a log rolling down a hill
all of the above