Physics Practice Problems

Question

The following questions refer to a pop-up toy with a mass of 0.35 kg. The toy's spring compresses 0.04 m, and has a spring constant of 3,000 N/m.

 

1. How high does the pop-up toy go?
2. What is the maximum speed of the pop-up toy?

 

Please show all work and explain using physics concepts.

Answer 1

1.  The entire potential energy of the spring is converted to gravitational potential energy.

 

(1/2)kx^2 = mgh

 

h = kx^2 / (2mg) = (3000)(0.04)^2 / [2(0.35)(9.8)] m = 0.700 m

 

 

2.  The entire potential energy of the spring is converted to kinetic energy.

 

(1/2)kx^2 = (1/2)mv^2

 

v = sqrt(kx^2 / m) = sqrt[(3000)(0.04)^2 / (0.35)] m/s = 3.7 m/s