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?
0.5 m
1 m
2 m
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.
