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A 1 kg mass is attached to a spring with a spring constant of 200 N/m. What is t

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Question: A 1 kg mass is attached to a spring with a spring constant of 200 N/m. What is the maximum extension of the spring when the mass is released from rest?

Options:

  1. 0.5 m
  2. 1 m
  3. 2 m
  4. 0.25 m

Correct Answer: 0.5 m

Solution: 

Using Hooke\'s law, F = kx, where F = mg = 1 kg * 9.8 m/s² = 9.8 N. Thus, x = F/k = 9.8 N / 200 N/m = 0.049 m.

A 1 kg mass is attached to a spring with a spring constant of 200 N/m. What is t

Practice Questions

Q1
A 1 kg mass is attached to a spring with a spring constant of 200 N/m. What is the maximum extension of the spring when the mass is released from rest?
  1. 0.5 m
  2. 1 m
  3. 2 m
  4. 0.25 m

Questions & Step-by-Step Solutions

A 1 kg mass is attached to a spring with a spring constant of 200 N/m. What is the maximum extension of the spring when the mass is released from rest?
Correct Answer: 0.049 m
  • Step 1: Identify the mass attached to the spring, which is 1 kg.
  • Step 2: Calculate the force due to gravity acting on the mass using the formula F = mg, where g = 9.8 m/s². So, F = 1 kg * 9.8 m/s² = 9.8 N.
  • Step 3: Identify the spring constant, which is given as 200 N/m.
  • Step 4: Use Hooke's law, which states that the force exerted by a spring is F = kx, where k is the spring constant and x is the extension of the spring.
  • Step 5: Rearrange Hooke's law to find the extension x: x = F/k.
  • Step 6: Substitute the values into the equation: x = 9.8 N / 200 N/m.
  • Step 7: Calculate the maximum extension: x = 0.049 m.
  • Hooke's Law – The relationship between the force exerted by a spring and its extension, expressed as F = kx, where F is the force, k is the spring constant, and x is the extension.
  • Weight Calculation – The calculation of the weight of an object using the formula F = mg, where m is mass and g is the acceleration due to gravity.
  • Equilibrium Position – Understanding that the maximum extension occurs when the spring force equals the weight of the mass.
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