A spring-loaded toy uses a compressed spring to fire a marble out of a
tube. A force of 220 N compresses the spring by 0.14 m. Calculate the
elastic potential energy of the toy.
Using the knowledge that the elastic potential energy of a spring is equal to the area under an F vs x graph (which is where the equation Ee = 1/2 kx^2 comes from);
Elastic potential energy = 1/2 xF
So,
Elastic potential energy = 1/2 (0.14)(220)
Using the knowledge that the elastic potential energy of a spring is equal to the area under an F vs x graph (which is where the equation Ee = 1/2 kx^2 comes from);
Elastic potential energy = 1/2 xF
So,
Elastic potential energy = 1/2 (0.14)(220)
= 15.4
=15 J
To calculate the elastic potential energy of the toy, we can use the formula:
Elastic potential energy = (1/2) * k * x^2
Where:
k is the spring constant (also known as the stiffness constant)
x is the displacement or compression of the spring.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement:
Force (F) = k * x
Rearranging the equation, we get:
k = F / x
Given that the force (F) is 220 N and the displacement (x) is 0.14 m, we can substitute these values into the equation to find k:
k = 220 N / 0.14 m
k = 1571.43 N/m (rounded to two decimal places)
Now, we can substitute the value of k and x into the elastic potential energy equation:
Elastic potential energy = (1/2) * k * x^2
Elastic potential energy = (1/2) * 1571.43 N/m * (0.14 m)^2
Elastic potential energy = 19.61 J (rounded to two decimal places)
Therefore, the elastic potential energy of the toy is 19.61 Joules.
To calculate the elastic potential energy of the toy, you can use the formula for elastic potential energy:
Elastic potential energy = 0.5 * k * x^2
Where:
- k is the spring constant, which is a measure of the stiffness of the spring.
- x is the displacement of the spring from its original position.
In this case, the force applied to the spring is 220 N, and it compresses the spring by 0.14 m. To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring:
F = k * x
Rearranging this equation to solve for the spring constant gives:
k = F / x
Now, substitute the values into the equation:
k = 220 N / 0.14 m
k = 1571.43 N/m
Now that we have the spring constant, we can calculate the elastic potential energy:
Elastic potential energy = 0.5 * k * x^2
Elastic potential energy = 0.5 * 1571.43 N/m * (0.14 m)^2
Elastic potential energy = 0.5 * 1571.43 N/m * 0.0196 m^2
Elastic potential energy ≈ 15.421 J
Therefore, the elastic potential energy of the toy is approximately 15.421 J.