A spring has a spring constant of 42 N/m. How much work is required to stretch the spring 1.5 cm from its equilibrium position?
work= 1/2 k x^2 = 1/2 42N/m * (.0015m)^2
4.725
To calculate the work required to stretch a spring, we can use the formula:
Work = (1/2)kx^2
where:
- k is the spring constant
- x is the displacement from the equilibrium position
Given that the spring constant, k, is 42 N/m, and the displacement, x, is 1.5 cm, we need to convert the displacement to meters:
Displacement (x) = 1.5 cm = 0.015 meters
Now we can substitute the values into the formula:
Work = (1/2) * 42 N/m * (0.015 m)^2
Calculating this expression will give us the work required to stretch the spring.
To determine the work required to stretch the spring, you need to use Hooke's law, which relates the force applied to a spring to the displacement. Hooke's law is given by the equation:
F = -kx
Where:
F = Force applied to the spring
k = Spring constant
x = Displacement from the equilibrium position
In this case, the force applied to the spring can be found using Hooke's law:
F = -kx = -42 N/m * (0.015 m)
Simplifying this expression, we find that the force applied to the spring is:
F = -0.63 N
The work done on an object can be calculated using the formula:
Work = Force * Distance * cos(θ)
Since the displacement x is in the opposite direction of the force applied, the angle between the force and displacement is 180 degrees. Thus, the cosine of 180 degrees is -1:
Work = -0.63 N * (-0.015 m) * (-1)
= 0.00945 J
Therefore, the work required to stretch the spring 1.5 cm from its equilibrium position is approximately 0.00945 Joules.