A spring-powered launcher has a spring with a spring constant of 150 N/cm.The launcher is prepared to launch a projectile by compressing the spring by 5.00 cm.If the mass of the projectile is 5.00 grams,then what is the velocity of the projectile when it is launched from the launcher?
A) 90.6 m/s
B) 86.6 m/s
C) 75.5 m/s
D) 60.3 m/s
E) 56.6 m/s

Question

Quizplus · Accepted Answer

Using conservation of energy, we can find the velocity of the projectile when it is launched.
The potential energy stored in the compressed spring is:
U = (1/2)kx² = (1/2)(150 N/cm)(5.00 cm)² = 1875 J
This potential energy is converted to kinetic energy when the projectile is launched:
K = (1/2)mv²
Setting these two equal, we have:
(1/2)kx² = (1/2)mv²
Solving for v, we get:
v = sqrt((k/m)x²) = sqrt((150 N/cm)/(0.005 kg))(0.050 m) = 86.6 m/s, to two significant figures. Therefore, the answer is B.

A Spring-Powered Launcher Has a Spring with a Spring Constant