# Worksheet: Deformation of Springs

In this worksheet, we will practice using the formula F = kx to calculate the deformation of a spring, defining the spring constant as the resistance of a spring to deformation.

**Q9: **

The graph shows the length of a spring as the force applied to it changes. What is the magnitude of the spring constant?

**Q13: **

A rocket is launched from Earth, accelerating uniformly. Inside the rocket are control panels, and some of the controls contain springs. A spring in one of the controls that is vertically aligned has a force constant of 555 N/m. The spring is stretched by 2.5 cm under a load with a mass of 1.2 kg.

What is the downward force on the spring? Answer to one decimal place.

What is the rocket’s upward acceleration? Answer to one decimal place.

What was the extension of the spring before the rocket’s launch? Answer to the nearest millimeter.

**Q14: **

A spring with a mass of 1.6 kg is held horizontally at both ends, and a force of 3 N is exerted at each end, pulling on the ends of the spring. The spring has a constant of 75 N/m. It is then released and returns to its original length. Then, the spring is stretched again. The spring extends at the same rate as when it was initially stretched, and is stretched for the same amount of time, but when stretched for the second time, the right-hand pulls with a force of 4 N and the left-hand pulls with a force of 2 N.

How far does the spring extend the first time it is stretched?

How far does the spring extend the second time it is stretched?

At what rate does the spring accelerate to the right when it is stretched the second time?

**Q16: **

The graph shows how the extension of a spring changes with the force applied to it.

In which region of the graph does the spring have the lowest constant?

- A
- B
- C
- D
- E

In which region of the graph does the spring have the highest constant?

- A
- B
- C
- D
- E

In which region of the graph is the spring constant continuously changing?

- A only
- B only
- C
- D only
- E only

In which region of the graph is the spring’s extension increasing?

- A
- B only
- C only
- D only
- E only

In which region of the graph is only the reversible extension of the spring shown?

- A
- B
- C
- D

In which region of the graph is only the permanent extension of the spring shown?

- A
- B
- C
- D

**Q17: **

A suspended platform is part of the scaffolding around a skyscraper being built. On the platform is a 5 kg mass tool bag suspended from a spring with an extension of 20 cm that has a constant of 245 N/m. An accident occurs and the scaffolding structure under the platform suddenly breaks. The platform falls but is slowed as it falls by friction with surrounding scaffolding. The platform drops a distance of 2.5 m, during which its velocity changes from zero to 4.5 m/s, and then comes to rest in a negligible time. What is the extension of the spring when the platform has dropped by 2.5 m but not yet come to rest? Round your answer to the nearest centimeter.

**Q18: **

A wooden crate with a mass of 15 kg is pulled by a spring that is embedded in one of its faces, as shown in the diagram. The spring’s constant is 725 N/m. The man pulling the crate applies a force of 150 N
to it, but the box does not move. The man then pulls harder, exerting a force of 250 N. The crate then starts to accelerate at 1.75 m/s^{2}.

How far does the spring extend when the man first pulls it? Answer to the nearest centimeter.

While the box is accelerating, what is the size of the force that the spring exerts on the box?

While the box is accelerating, what is the size of the force that the box exerts on the spring?

While the box is accelerating, how far does the spring extend? Answer to the nearest centimeter.

**Q19: **

A child’s toy has a car that starts at rest and then accelerates down a slope and away from a
toy garage at an average rate of 1 m/s^{2}. The toy garage does not move. The car has
a mass of 125 g. A spring connects the car to the garage, and the spring is at its unstretched
length before the car starts to roll down the slope.

What average force acts on the car in the direction of the slope over the car’s first second of motion?

How far along the slope does the car move in its first second of motion?

What is the magnitude of the spring constant in the first second of the car’s motion?