a spring exerts a force of 150 N when it is stretched 0.4 m beyond its natural length. How much work is required to stretch the spring 0.9 m beyond its natural length?
41
To find the work required to stretch the spring, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed.
Hooke's Law equation is given by:
F = k * x
Where:
F = Force exerted by the spring (in N)
k = Spring constant (in N/m)
x = Distance stretched or compressed from the natural length (in m)
In this case, we are given that the spring exerts a force of 150 N when stretched by 0.4 m. We can use this information to calculate the spring constant.
150 N = k * 0.4 m
Dividing both sides of the equation by 0.4 m:
k = 150 N / 0.4 m = 375 N/m
Now that we have the spring constant (k), we can calculate the force required to stretch the spring by 0.9 m.
F = k * x
F = 375 N/m * 0.9 m
F = 337.5 N
The force required to stretch the spring by 0.9 m beyond its natural length is 337.5 N.
To find the work done, we can use the work formula:
Work (W) = Force (F) * Distance (d) * cos(theta)
In this case, the force required is 337.5 N, and the distance stretched is 0.9 m. Since the force and distance are in the same direction, the angle between them is 0 degrees, and thus the cos(theta) is equal to 1.
Work (W) = 337.5 N * 0.9 m * cos(0)
Work (W) = 337.5 N * 0.9 m * 1
Work (W) = 303.75 Joules
Therefore, the work required to stretch the spring 0.9 m beyond its natural length is 303.75 Joules.