A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #12 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

Question

A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3  kg# and speed of #12 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

Sebastian Acosta · Accepted Answer

The compression is #=9.3m#

The spring constant is #k=5kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=3kg#

The speed is #u=12ms^-1#

#KE=1/2*3*(12)^2=216J#

This kinetic energy will be stored in the spring as potential energy.

#PE=216J#

So,

#1/2kx^2=216#

#x^2=(2*216)/(5)=86.4m^2#

#x=sqrt(86.4)=9.3m#

Carson Alexander · Answer

undefined To find the compression of the spring, you can use the conservation of mechanical energy. The initial kinetic energy of the object is equal to the potential energy stored in the compressed spring.

1. Calculate the initial kinetic energy of the object.
2. Use the spring constant and the formula for potential energy stored in a spring to find the compression.

Initial kinetic energy = 0.5 * mass * velocity^2
Potential energy stored in the spring = 0.5 * spring constant * compression^2

Set the initial kinetic energy equal to the potential energy stored in the spring and solve for compression.