Suppose the spring in this spring-powered rifle has a spring constant of k = 1,000 N/m. How much work can it do in accelerating the projectile, if it is compressed by x = 0.10 m?
5.0j
To calculate the work done by the spring in accelerating the projectile, we can use the formula for the potential energy stored in a spring:
Potential energy (U) = (1/2) * k * x²
Where:
- k is the spring constant, given as 1,000 N/m.
- x is the displacement of the spring from its equilibrium position, given as 0.10 m.
First, let's substitute the given values into the formula:
U = (1/2) * (1,000 N/m) * (0.10 m)²
Now, let's simplify the equation:
U = (1/2) * 1,000 N/m * 0.01 m²
= 0.5 * 1,000 N/m * 0.01 m²
= 0.5 * 10 N * 0.01 m
= 0.5 N * 0.1 m
= 0.05 N * m
= 0.05 J
Therefore, the spring can do 0.05 Joules of work in accelerating the projectile when it is compressed by 0.10 meters.
To find the work done by the spring in accelerating the projectile, we can use the formula for the potential energy stored in a spring:
Potential energy (U) = 0.5 * k * x^2
Given:
Spring constant (k) = 1,000 N/m
Compression distance (x) = 0.10 m
Substituting the given values into the formula:
Potential energy (U) = 0.5 * 1000 * (0.10)^2
= 0.5 * 1000 * 0.01
= 5 N.m
The work done by the spring in accelerating the projectile is equal to the potential energy stored in the spring. Therefore, the work done is 5 N.m.