A spring-powered launcher has a spring with a constant of 150 N/cm. The launcher is prepared by compressing the spring by 5.00 cm. If the mass of the projectile is 5.00 grams, what is the speed of the projectile when it is launched?
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

The potential energy stored in the spring when it is compressed is given by:
$$U = \frac{1}{2}kx^2$$
where $k$ is the spring constant and $x$ is the compression distance. Substituting the given values:
$$U = \frac{1}{2}(150\,	ext{N/cm})(5.00\,	ext{cm})^2 = 1875\,	ext{J}$$
This potential energy is converted into kinetic energy of the projectile when the spring is released. The kinetic energy of an object with mass $m$ moving at speed $v$ is given by:
$$K = \frac{1}{2}mv^2$$
Since energy is conserved, we can equate the potential energy stored in the spring to the kinetic energy of the projectile:
$$K = U = 1875\,	ext{J}$$
Substituting the given mass of the projectile:
$$\frac{1}{2}(0.005\,	ext{kg})v^2 = 1875\,	ext{J}$$
Solving for $v$ gives:
$$v = \sqrt{\frac{2(1875\,	ext{J})}{0.005\,	ext{kg}}} \approx 86.6\,	ext{m/s}$$
Therefore, the correct answer is B.

A Spring-Powered Launcher Has a Spring with a Constant of 150