A spring with constant speed of 3.5x10^4 N/m is initially @ its equilibrium length. (a)How much work must u do to stretch the spring 0.050 m? (b) How much work must you do to crompress it 0.050m?
Energyinspring= 1/2 k*deflection^2
you are given the deflection, and k.
(1/2)(3.5x10^4 N/m)(0.050m)^2
(a) How much work must u do to stretch the spring 0.050 m?
Well, according to Hooke's Law, the force required to stretch or compress a spring is given by the formula F = kx, where F is the force, k is the spring constant, and x is the displacement.
So, in this case, the force required to stretch the spring by 0.050 m would be F = (3.5x10^4 N/m) * (0.050 m).
Now, to find the work done, we can use the formula W = 0.5 * k * x^2, where W is the work done, k is the spring constant, and x is the displacement.
Plugging in the values, we have W = 0.5 * (3.5x10^4 N/m) * (0.050 m)^2.
So, the work done to stretch the spring by 0.050 m would be W = 43.75 J.
(b) How much work must you do to compress it 0.050m?
The force required to compress a spring is the same as the force required to stretch it, but in the opposite direction. So, the force would still be F = (3.5x10^4 N/m) * (0.050 m).
Using the same formula as before, W = 0.5 * k * x^2, we can find the work done to compress the spring by 0.050 m.
Plugging in the values, we have W = 0.5 * (3.5x10^4 N/m) * (0.050 m)^2.
Therefore, the work done to compress the spring by 0.050 m would also be W = 43.75 J.
Now, isn't it fascinating how the work done is the same for both stretching and compressing the spring? It's almost like the spring is just clowning around with us!
To calculate the work done to stretch or compress the spring, we can use the formula:
Work = (1/2) * k * x^2
Where:
- k is the spring constant
- x is the displacement from the equilibrium position
(a) To find the work done to stretch the spring, we substitute the given values into the formula:
k = 3.5 × 10^4 N/m
x = 0.050 m
Work = (1/2) * (3.5 × 10^4 N/m) * (0.050 m)^2
Calculating the above expression, we get:
Work = 43.75 J
Therefore, the work done to stretch the spring by 0.050 m is 43.75 J.
(b) To find the work done to compress the spring, we use the same formula but with a negative displacement value (-0.050 m):
k = 3.5 × 10^4 N/m
x = -0.050 m
Work = (1/2) * (3.5 × 10^4 N/m) * (-0.050 m)^2
Calculating the above expression, we get:
Work = -43.75 J
Therefore, the work done to compress the spring by 0.050 m is -43.75 J.
To find the work done in both stretching and compressing the spring, we can use the formula:
Work = (1/2) * k * x^2
Where:
- Work is the amount of work done in stretching or compressing the spring (measured in joules, J).
- k is the spring constant (measured in newtons per meter, N/m).
- x is the displacement from the equilibrium position (measured in meters, m).
(a) To find the work done in stretching the spring by 0.050 m:
Given:
- k = 3.5 × 10^4 N/m (spring constant)
- x = 0.050 m (displacement)
Using the formula:
Work = (1/2) * k * x^2
Substituting the given values:
Work = 0.5 * (3.5 × 10^4 N/m) * (0.050 m)^2
Calculate the answer:
Work = 43.75 J
Therefore, the work done to stretch the spring by 0.050 m is 43.75 joules.
(b) To find the work done in compressing the spring by 0.050 m:
Since work is a scalar quantity, the work done in compressing the spring by the same amount will be the same as the work done in stretching it.
Therefore, the work done to compress the spring by 0.050 m is also 43.75 joules.