Question

1.A mother has four times the mass of her young son. Both are running with the same kinetic energy.

What is the ratio vs/vm other of their speeds?
2.How far must you stretch a spring with k = 1000N/m to store 240J of energy?

Answer 1

the son is running 2 times faster

You must stretch it 0.6928 meters

Step-by-step explanation:

Kinetic energy is 1/2*mv^2, meaning doubling the velocity of something, quadruples the kinetic energy.

1/2 * (4m)*v^2=1/2*m*(2v)^2 as these both simplify down to 2mv^2

Storing energy means potential energy.

The formula for the potential energy of a spring is 1/2*k*x^2,

240=1/2*1000*x^2

240/500=x^2

x=sqrt(.48)

x=.6928.