A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the w
Practice Questions
Q1
A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the work done in compressing the spring?
25 J
50 J
100 J
200 J
Questions & Step-by-Step Solutions
A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the work done in compressing the spring?
Correct Answer: 25 J
Step 1: Identify the spring constant (k). In this case, k = 200 N/m.
Step 2: Identify the compression distance (x). Here, x = 0.5 m.
Step 3: Use the formula for work done on a spring: Work done = 0.5 × k × x².
Step 4: Substitute the values into the formula: Work done = 0.5 × 200 N/m × (0.5 m)².
Step 5: Calculate (0.5 m)², which equals 0.25 m².
Step 6: Multiply 200 N/m by 0.25 m², which equals 50 N·m.
Step 7: Finally, multiply 50 N·m by 0.5, which equals 25 J.
Hooke's Law and Work Done on Springs – The work done in compressing or stretching a spring is calculated using the formula W = 0.5 × k × x², where k is the spring constant and x is the displacement from the equilibrium position.
