Suppose a 0.30-kg mass on a spring-loaded gun that has been compressed 0.10 m has elastic potential energy of 1.0 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?
A)0.10 m
B)0.34 m
C)0.24 m
D)10 m

Question

Quizplus · Accepted Answer

The elastic potential energy of the spring is converted into gravitational potential energy of the mass as it is fired upward. By conservation of energy, we can equate the two types of energy:
1.0 J = mgh
where m is the mass, g is the acceleration due to gravity, and h is the maximum height reached. Solving for h:
h = 1.0 J / (0.30 kg × 9.81 m/s²) = 0.34 m
However, this is the total distance traveled by the mass, not the height above the spring's equilibrium point. Since the spring was compressed 0.10 m, the height above its equilibrium point is:
0.34 m - 0.10 m = 0.24 m
Therefore, the correct answer is (C).