13.2.A.2Multiple Choice
A student pushes a crate 8 m across a floor with a constant horizontal force of 40 N in the direction of motion. How much work does the student do on the crate?
Select A, B, C, or D to check your answer.
Directions:Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 3.2 — conservative/nonconservative forces, the scalar nature of work, the dot-product and parallel-component definition of work, the work–energy theorem, and work as the area under a force–displacement graph. Round decimals to the nearest tenth unless noted otherwise.
A student pushes a crate 8 m across a floor with a constant horizontal force of 40 N in the direction of motion. How much work does the student do on the crate?
Select A, B, C, or D to check your answer.
A 2 kg block slides from rest down a curved, frictionless ramp and reaches the bottom at 4 m/s. (a) Is gravity, here, doing conservative or nonconservative work? Explain using the shape of the ramp. (b) If a second, identical block slides down a differently-shaped frictionless ramp of the same height, what speed will it have at the bottom? (c) Explain your answer to (b) in terms of path-independence.
A hiker carries a backpack along a winding, hilly trail and ends up back at the exact point where she started, at the same elevation. Which force did zero net work on the backpack over the entire round trip?
Select A, B, C, or D to check your answer.
A rope pulls a 10 kg sled 5 m across level, frictionless snow with a tension of 60 N directed 5° above the horizontal. At the same time, air resistance exerts 15 N directly opposing the sled's motion. (a) Find the work done by the rope's tension. (b) Find the work done by air resistance. (c) Find the total (net) work done on the sled, and state whether it is positive, negative, or zero.
| Force | magnitude (N) | angle to displacement |
| Tension | 60 | 5° |
| Air resistance | 15 | 180° |
A satellite moves in a circular orbit at constant speed, held in its path by gravity, which points toward the center of the orbit at every instant. How much work does gravity do on the satellite over one full orbit?
Select A, B, C, or D to check your answer.
A variable force acts on a 1 kg cart along a straight track according to F(x) = 6x (in newtons, with x in meters). (a) Set up the work integral for the work done as the cart moves from x = 0 to x = 4 m. (b) Evaluate the integral. (c) Explain why you could not simply use W = Fd here without integrating.
A 1500 kg car, starting from rest, is accelerated by a net horizontal force of 4500 N over a distance of 20 m on a level road. Using the work–energy theorem, what is the car's final speed?
Select A, B, C, or D to check your answer.
A 4 kg box slides across a rough horizontal floor, slowing from 8 m/s to 5 m/s over a distance of 3 m. (a) Find the box's change in kinetic energy. (b) Use the work–energy theorem to find the net work done on the box. (c) Find the magnitude of the friction force, assuming friction is the only horizontal force acting.
A person pulls themself up a vertical climbing rope, hand over hand, and gains kinetic energy and height in the process. The rope does not stretch and the point where each hand grips the rope does not slide. Which statement correctly describes why the work–energy theorem must be applied carefully here?
Select A, B, C, or D to check your answer.
The graph shows the parallel component of a varying force, F∥, acting on an object as it moves along the x-axis, from x = 0 to x = 6 m. The force is +10 N from x = 0 to x = 3 m, then decreases linearly to 0 N at x = 6 m. (a) Find the work done over the first 3 m. (b) Find the work done over the next 3 m. (c) Find the total work done from x = 0 to x = 6 m.
A force of 25 N acts perpendicular (90°) to an object's 6 m displacement. How much work does this force do on the object?
Select A, B, C, or D to check your answer.
A skier slides down a snowy slope, experiencing both gravity and kinetic friction from the snow. (a) Classify gravity and friction here as conservative or nonconservative, with a reason for each. (b) Which of the two forces is associated with a potential energy function, and why? (c) If the skier takes a longer, more winding path down to the same final point at the base, will the work done by gravity change? Will the work done by friction change? Explain.
A 20 N force is applied to a box at an angle of 60° above the direction of the box's 4 m horizontal displacement. What is the work done by this force?
Select A, B, C, or D to check your answer.
A 1200 kg car travels at 15 m/s when the driver applies the brakes, which exert a constant friction force of 4500 N, brought the car to a stop. (a) Find the car's initial kinetic energy. (b) Use the work–energy theorem to find the stopping distance. (c) If the car had instead been traveling at twice the speed (30 m/s) with the same braking force, would the stopping distance also double? Justify your answer numerically.
The graph shows a force F∥ that is +8 N from x = 0 to x = 2 m, then switches to −8 N from x = 2 m to x = 5 m. What is the total work done from x = 0 to x = 5 m?
Select A, B, C, or D to check your answer.
A compressed spring launches a 0.3 kg ball. As the spring pushes the ball, (a) is the spring force conservative or nonconservative? Explain in terms of energy storage. (b) Once the ball leaves the spring and flies through the air, what nonconservative force acts on it, and what happens to the mechanical energy it removes? (c) Suppose instead a rubber band (also elastic, but with significant internal friction as it stretches) launches an identical ball with the same initial stored energy. Would you expect the ball to leave with the same speed as with the spring? Explain.
A tugboat applies a constant 8000 N force to a barge at an angle θ above the barge's line of motion. As θ increases from 0° toward 90° (with the force magnitude and the distance traveled both held fixed), what happens to the work done by the tugboat on the barge?
Select A, B, C, or D to check your answer.
A 1500 kg car accelerates from 10 m/s to 25 m/s over a distance of 100 m due to the net force from its engine and the road. (a) Find the car's change in kinetic energy. (b) Use the work–energy theorem to find the net force on the car, assuming it is constant. (c) If instead the same net force acted over only half the distance (50 m) starting from the same 10 m/s, what would the car's final speed be?
An object experiences a force F∥ that varies with position as shown: the graph is a straight line starting at +12 N at x = 0 m and decreasing linearly to 0 N at x = 4 m. What is the work done as the object moves from x = 0 to x = 4 m?
Select A, B, C, or D to check your answer.
A 5 kg block is pushed 6 m across a rough horizontal floor by a constant applied force of 40 N directed 30° above horizontal, while kinetic friction of 12 N acts on the block (opposing its motion). (a) Find the work done by the applied force. (b) Find the work done by friction. (c) Find the net work done on the block, and use the work–energy theorem to find its final speed, given that it started at rest. (d) Suppose instead the same scenario occurred on a frictionless floor (friction = 0 N). Would the block's final speed be larger, smaller, or the same? Find the new final speed to support your answer.