The spring on a popgun obeys Hooke's law and requires a force of 220 N to compress it 12.0 cm to its cocked position. How much energy is stores in the cocked spring?
To find the amount of energy stored in the cocked spring, you can use the formula for potential energy stored in a spring:
Potential Energy (PE) = (1/2) * k * x^2
where k is the spring constant and x is the displacement.
In this case, the force required to compress the spring is 220 N, and the displacement is 12.0 cm (which is 0.12 m). Since Hooke's law states that F = k * x, we can rearrange the equation to find the spring constant:
k = F / x
k = 220 N / 0.12 m
Now, substitute the values into the potential energy equation:
PE = (1/2) * k * x^2
PE = (1/2) * (220 N / 0.12 m) * (0.12 m)^2
PE = (1/2) * (220 N / 0.12 m) * (0.0144 m^2)
PE = (1/2) * (220 N / 0.12) * (0.0144 m^2)
PE = (1/2) * (1833.33 N/m) * (0.0144 m^2)
PE ≈ 11.11 Joules
Therefore, the amount of energy stored in the cocked spring is approximately 11.11 Joules.
To determine the energy stored in the cocked spring, we can use the formula for potential energy in a spring.
The potential energy stored in a spring can be calculated using the equation:
E = 1/2 * k * x²
where E represents the energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, we are given the force required to compress the spring (220 N) and the displacement (12.0 cm). However, the spring constant (k) is not provided directly.
We can find the spring constant (k) by rearranging Hooke's law equation:
F = k * x
where F is the applied force and x is the displacement. Rearranging this equation, we have:
k = F / x
Now we can substitute the values into the equations.
k = 220 N / 0.12 m (Note: convert cm to meters by dividing by 100)
k = 1833.33 N/m
Next, we can use the value of the spring constant to calculate the energy stored in the cocked spring:
E = 1/2 * 1833.33 N/m * (0.12 m)²
E = 13.2 J
Therefore, the energy stored in the cocked spring is 13.2 Joules.