A spring with a spring constant k = 50N/m has an unstretched length of 20cm. Find the work required to stretch the spring to a length of 30 cm.
W = J ?? any help guys?
Consider the formula for the potential energy of a stretched or compressed spring.
P.E. = (1/2) k X^2
The work required equals the potential energy increase. In your case the amount of stretching is X=0.10 meter
Yes, you are correct. The work required to stretch a spring can be found using the formula:
W = (1/2) * k * (Δx)^2
Where:
W is the work done (in joules),
k is the spring constant (in newtons per meter),
Δx is the change in length of the spring (in meters).
In this case, the spring constant (k) is given as 50 N/m, and the change in length (Δx) is 30 cm - 20 cm = 10 cm = 0.1 m.
Plugging these values into the formula, we get:
W = (1/2) * 50 N/m * (0.1 m)^2
W = (1/2) * 50 N/m * 0.01 m^2
W = 0.5 N * 0.01 m
W = 0.005 J
Therefore, the work required to stretch the spring to a length of 30 cm is 0.005 joules.
To find the work required to stretch the spring, we can use the formula for work:
W = (1/2) k x^2
Where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, we need to find the work done to stretch the spring from an unstretched length of 20cm to a length of 30cm.
First, we need to find the displacement of the spring:
x = final length - initial length
x = 30cm - 20cm
x = 10cm
Now we can substitute the values into the formula:
W = (1/2) k x^2
W = (1/2) x (50N/m) x (10cm)^2
(Note: To convert cm to meters, we need to divide by 100 since 1m = 100cm. So 10cm = 0.1m)
W = (1/2) x (50N/m) x (0.1m)^2
W = (1/2) x 50N/m x 0.01m^2
W = (1/2) x 50N/m x 0.01m^2
W = (1/2) x 50N/m x 0.0001m
W ≈ 0.00025 J
Therefore, the work required to stretch the spring to a length of 30 cm is approximately 0.00025 Joules.