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.

Q1:

A spring with a force constant of 64 N/m is pulled by a force of 4.8 N. By how many centimeters does the length of the spring increase?

Q2:

A spring with a constant of 700 N/m is stretched when a force of 35 N is applied to it, and its length when stretched is 0.48 m. What is the spring’s length when it is not extended?

Q3:

A spring that is 0.36 m long is pulled by a force of 18 N. The spring’s length increases by 0.012 m. What is the constant of the spring?

Q4:

A 0.28 m long spring with a force constant of 25 N/m is compressed by a force of 1.25 N. What is the length of the compressed spring?

  • A 0.2 m
  • B 0.33 m
  • C 0.48 m
  • D 0.23 m
  • E 0.38 m

Q5:

A spring with a constant of 120 N/m is 0.35 m long when unloaded. A force is exerted on the end of the spring and the spring’s length changes to 0.45 m. What is the magnitude of the force exerted on the end of the spring?

Q6:

A spring increases in length by 0.25 m when a force is applied to it. The spring has a constant of 40 N/m. What is the magnitude of the force exerted on the spring?

Q7:

Which of the following is a correct unit of a spring constant?

  • A m/N2
  • B N⋅m
  • C N⋅m2
  • D N/m
  • E N2/m

Q8:

Which of the following formulas correctly shows the relation between the force applied to a spring, the change in the spring’s length Δ 𝑥 , and the spring constant (also known as stiffness) of spring 𝑘 ?

  • A 𝐹 = 𝑥 Δ 𝑘
  • B 𝐹 = 𝑘 Δ 𝑥
  • C 𝐹 = 1 2 𝑘 Δ 𝑥 2
  • D 𝐹 = 𝑘 Δ 𝑥
  • E 𝐹 = 1 𝑘 Δ 𝑥

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q15:

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

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
  • B 𝐴 𝐵
  • C 𝐴 𝐶
  • D 𝐶 𝐷
  • E 𝐴 𝐷

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

  • A 𝐴 𝐵
  • B 𝐴 𝐷
  • C 𝐵 𝐶
  • D 𝐶 𝐷
  • E 𝐵 𝐷

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

  • A 𝐴 𝐶 only
  • B 𝐴 𝐵 only
  • C 𝐴 𝐷
  • D 𝐶 𝐷 only
  • E 𝐵 𝐶 only

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

  • A 𝐴 𝐷
  • B 𝐴 𝐶 only
  • C 𝐶 𝐷 only
  • D 𝐴 𝐵 only
  • E 𝐵 𝐶 only

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

  • A 𝐴 𝐷
  • B 𝐶 𝐷
  • C 𝐵 𝐶
  • D 𝐴 𝐵

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

  • A 𝐵 𝐶
  • B 𝐶 𝐷
  • C 𝐴 𝐵
  • D 𝐴 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/s2.

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.

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