A spring-powered dart gun is unstretched and has a spring constant 10.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is
A) 0.020 J.
B) 0.032 J.
C) 0.060 J.
D) 0.100 J.
E) 0.120 J.

Question

Quizplus · Accepted Answer

The kinetic energy of the projectile can be calculated using the formula for the potential energy stored in a compressed spring, which is given by $PE = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the compression distance. Here, $k = 10.0 \, \text{N/m}$ and $x = 8.00 \, \text{cm} = 0.080 \, \text{m}$. Plugging these values into the formula gives $PE = \frac{1}{2} \times 10.0 \, \text{N/m} \times (0.080 \, \text{m})^2 = 0.032 \, \text{J}$. This potential energy is converted into kinetic energy as the projectile is shot from the gun, so the kinetic energy of the projectile is 0.032 J.

A Spring-Powered Dart Gun Is Unstretched and Has a Spring