how much energy is stored in a pinball machine spring (constant=750N/m) that is compressed 3 cm?
What is 1/2 k *.03^2 Joules?
3 cm = .03 meters
E = (1/2) k x^2
E = (1/2)(750)(.0009) Joules
To calculate the energy stored in a compressed spring, you can use the formula:
E = (1/2)kx^2
where:
E is the energy stored in the spring,
k is the spring constant,
x is the compression or elongation of the spring.
In this case, the spring constant (k) is given as 750 N/m and the compression (x) is 3 cm. However, we need to convert the compression from centimeters to meters before plugging it into the formula.
1 cm = 0.01 m
Therefore, the compression (x) in meters is:
x = 3 cm * 0.01 m/cm = 0.03 m
Now we can calculate the energy stored in the spring:
E = (1/2) * 750 N/m * (0.03 m)^2
E = (1/2) * 750 N/m * (0.0009 m^2)
E = 0.3375 Joules
So, the energy stored in the pinball machine spring is approximately 0.3375 Joules.
To calculate the amount of energy stored in a spring that is compressed, you can use the formula for potential energy stored in a spring:
Potential Energy (PE) = (1/2) * k * x^2
Where:
- PE is the potential energy (or stored energy) in joules
- k is the spring constant in newtons per meter (N/m)
- x is the displacement (or compression) of the spring in meters (m)
In this case, the spring constant (k) is given as 750 N/m, and the displacement (x) is 3 cm, which is equivalent to 0.03 meters.
Now, let's substitute the values into the formula and calculate the potential energy:
PE = (1/2) * 750 N/m * (0.03 m)^2
PE = (1/2) * 750 N/m * 0.0009 m^2
PE = 0.5 * 750 N/m * 0.0009 m^2
PE = 0.5 * 675 N * (1 m^2 / 1000 N)
PE = 0.5 * 0.675 Nm
PE = 0.3375 J
Therefore, the energy stored in the compressed pinball machine spring is approximately 0.3375 joules.