A spring with a force constant of 5.4 N/m has
a relaxed length of 2.63 m. When a mass is
attached to the end of the spring and allowed
to come to rest, the vertical length of the
spring is 3.64 m.
Calculate the elastic potential energy
stored in the spring.
Answer in units of J Your answer must be
within
±
1.0%
(1/2) k x^2
(1/2)(5.4)(3.64-2.63)^2
2.75427 Joules
Well, it seems like this spring has really stretched out! It's like it's reaching for the stars...or at least the ceiling. Let's calculate the elastic potential energy stored in this spring.
The formula for elastic potential energy is U = (1/2) k x^2, where U is the elastic potential energy, k is the force constant, and x is the displacement from the relaxed length.
Given that the force constant is 5.4 N/m and the displacement of the spring is 3.64 m - 2.63 m = 1.01 m, we can plug in these values into the formula:
U = (1/2) * 5.4 N/m * (1.01 m)^2
Calculating this out, the elastic potential energy stored in the spring is approximately 2.74 J.
Remember, laughter is like elastic potential energy - it has the power to spring you back into action!
To calculate the elastic potential energy stored in the spring, we can use the formula:
Elastic potential energy (PE) = (1/2)kx^2
Where:
- k is the force constant of the spring
- x is the displacement from the relaxed length of the spring.
First, we need to find the displacement of the spring, x. This can be calculated by subtracting the relaxed length from the vertical length when the mass is attached:
x = vertical length - relaxed length
x = 3.64 m - 2.63 m
x = 1.01 m
Now, we can calculate the elastic potential energy:
PE = (1/2) * k * x^2
PE = (1/2) * 5.4 N/m * (1.01 m)^2
PE = (1/2) * 5.4 N/m * 1.0201 m^2
PE = 0.510 N/m * m^2
PE = 0.510 J
Therefore, the elastic potential energy stored in the spring is approximately 0.510 J.
To calculate the elastic potential energy stored in the spring, we can use the formula:
Elastic Potential Energy (PE) = 0.5 * k * (x^2)
Where:
- PE is the elastic potential energy stored in the spring
- k is the force constant of the spring
- x is the displacement from the relaxed length
First, we need to find the displacement of the spring. We can do this by subtracting the relaxed length from the vertical length:
Displacement (x) = Vertical Length - Relaxed Length
x = 3.64 m - 2.63 m
x = 1.01 m
Next, we can substitute the values into the formula:
PE = 0.5 * k * (x^2)
PE = 0.5 * 5.4 N/m * (1.01 m)^2
Calculating this:
PE = 0.5 * 5.4 N/m * 1.0201 m^2
PE = 2.697 J
Therefore, the elastic potential energy stored in the spring is approximately 2.697 J.