Question

You pull the plunger back on a pinball machine. The spring is pulled back 25 cm from its rest position and has a spring constant of 78 N/m. What speed will a 50.0 g ball in front of the spring reach when the spring has returned to its rest position?

Answer 1

Answer:

9.9 m/s

Explanation:

from the question we are given the following

length (L) = 25cm = 25 / 100 = 0.25m

spring constant (K) = 78 N/m

mass of the ball (m) = 50g = 50 / 1000 = 0.05 kg

At maximum compression all energy is potential energy and at maximum velocity all energy is kinetic energy, and from the conservation of energy the two energy must be he same. Therefore

potential energy at max compression = kinetic energy at max velocity

(1/2) x K x L^2 = (1/2) x m x V^2

(1/2) x 78 x 0.25^2 = (1/2) x 0.05 x V^2

V^2 = 97.6

V =  9.9 m/s