Answer to Question #119783 in Mechanics | Relativity for Noah

Question

A catapult has a spring constant of 20 N/m and is pulled back 5 cm.
Calculate the initial speed of the projectile if it has a mass of 0.1 kg.

Answer 1

We can find the initial speed of the projectile from the law of conservation of energy (the potential energy stored in the spring is converted itno the kinetic energy of the projectile):

$$PE_{spring} = KE_{projectile},$$ $$\dfrac{1}{2}kx^2 = \dfrac{1}{2}mv^2,$$ $$v = \sqrt{\dfrac{kx^2}{m}} = \sqrt{\dfrac{20 \ \dfrac{N}{m} \cdot (0.05 \ m)^2}{0.1 \ kg}} = 0.707 \ \dfrac{m}{s}.$$

Answer:

$v = 0.707 \ \dfrac{m}{s}.$