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Forces and Motion Worksheets

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Forces and Motion Worksheets

Aotearoa’s alpine rescue team is testing a winch system to move equipment safely. Use g = 9.8 m s⁻² unless stated otherwise. Show equations, substitutions, units and direction conventions. Assume ideal ropes and negligible air resistance where relevant.

Winch test data

A rescue sled and its equipment have a combined mass of 80 kg. The sled is pulled up a 20° slope by a cable parallel to the slope. The cable tension is 500 N, and the slope exerts a 70 N friction force down the slope.

1.For the sled, calculate the component of its weight parallel to the slope. Take up the slope as positive. What is the net force along the slope?

2.Use the net force to calculate the sled’s acceleration. Include its direction.

3.Which set of forces belongs on a free-body diagram of the moving sled? Select the correct option.

Tension up the slope; friction down the slope; normal force perpendicular to the slope; weight vertically downwards.
Tension vertically upwards; friction vertically downwards; normal force horizontally; weight up the slope.
Tension and friction both up the slope; normal force vertically upwards; weight perpendicular to the slope.

4.Calculate the normal force on the sled. Explain why the cable tension and friction do not affect your perpendicular-to-slope force balance.

A change in the test

The team reduces cable tension to 300 N while the sled is still moving up the slope. The friction force remains 70 N.

5.Calculate the new acceleration, taking up the slope as positive. Interpret the sign of your result.

6.At the instant the tension changes, the sled is travelling up the slope at 4.0 m s⁻¹. Assuming the new acceleration stays constant, how long until it momentarily stops?

7.For the same slowing phase, calculate how far the sled travels up the slope before stopping.

8.A trainee says, “The sled is moving up the slope, so its acceleration must also be up the slope.” Explain why this is incorrect using the reduced-tension situation.

Winch motion record

The sled begins at rest. Its velocity increases uniformly to 4.0 m s⁻¹ over 2.0 s, then remains at 4.0 m s⁻¹ for 3.0 s. Treat the motion as along the slope.

9.Sketch a velocity–time graph for the 5.0 s record. Label both axes and show the changing and constant-velocity sections.

10.Find the total distance travelled during the 5.0 s record. Use the area under your velocity–time graph.

11.The sled and its equipment are replaced by a 100 kg load. The slope angle, cable tension (500 N) and friction force (70 N) stay the same. Calculate its acceleration up the slope and explain why the acceleration changes.