A spring has a spring constant of 25N/m .
Part A
How much work is required to stretch the spring 2.0cm from its equilibrium position?
k=25, x=2cm=0.02m
w=1/2*k*x^2
To calculate the work required to stretch a spring, we can use the formula:
Work = (1/2) * k * (x^2)
where:
- Work is the amount of work done on the spring (in joules)
- k is the spring constant (in newtons per meter, N/m)
- x is the displacement of the spring from its equilibrium position (in meters)
In this case, we are given:
- k = 25 N/m
- x = 2.0 cm = 0.02 m (since 1 cm = 0.01 m)
Substituting these values into the formula, we get:
Work = (1/2) * 25 N/m * (0.02 m)^2
Calculating this expression:
Work = (1/2) * 25 N/m * (0.0004 m^2)
= 0.5 * 25 N/m * 0.0004 m^2
= 0.5 * 25 N/m * 0.0004 m^2
= 0.5 * 0.01 N * 0.0004 m^2
= 0.005 N * 0.0004 m^2
= 0.002 N * m
Therefore, the amount of work required to stretch the spring 2.0 cm from its equilibrium position is 0.002 N·m (or 0.002 joules).