A force of 543 N keeps a certain spring stretched a distance of 0.700 m .
Part A
What is the potential energy of the spring when it is stretched 0.700 m ?
Express your answer with the appropriate units.
k = force/distance = 543/.7
U = (1/2) k x^2 = (1/2) k (.7)^2 = (1/2) (543)(.7^2)/.7
= (1/2)(543)(.7) = average force * distance of course
Newtons * meters = Joules
The potential energy of a spring can be calculated using the formula:
Potential energy = (1/2) k x^2
Where:
k = spring constant
x = displacement
Given:
Force (F) = 543 N
Displacement (x) = 0.700 m
To find the spring constant (k), we can rearrange Hooke's Law formula as:
F = k x
Therefore, we have:
543 N = k * 0.700 m
Solving for k:
k = 543 N / 0.700 m
k ≈ 776.43 N/m
Now we can find the potential energy using the formula:
Potential energy = (1/2) k x^2
Substituting the values:
Potential energy = (1/2) * 776.43 N/m * (0.700 m)^2
Calculating:
Potential energy ≈ 188.47 J
Therefore, the potential energy of the spring when it is stretched 0.700 m is approximately 188.47 J (joules).
To answer this question, we need to use the formula for potential energy stored in a spring:
Potential Energy = (1/2) * k * x^2
Where:
- Potential Energy is the energy stored in the spring (in joules, J)
- k is the spring constant (in newtons per meter, N/m)
- x is the displacement of the spring from its equilibrium position (in meters, m)
Given:
- Force applied to the spring, F = 543 N
- Displacement, x = 0.700 m
First, we need to find the spring constant, k. We can use Hooke's Law to do that:
F = k * x
Rearranging the equation, we can solve for k:
k = F / x
Substituting the given values, we can find the spring constant:
k = 543 N / 0.700 m
Now, we can substitute the spring constant and displacement into the formula for potential energy:
Potential Energy = (1/2) * k * x^2
Substituting the values:
Potential Energy = (1/2) * (543 N / 0.700 m) * (0.700 m)^2
Calculating this expression will give us the answer for the potential energy of the spring.