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 #6 kg# and speed of #2 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

2 Answers
Mar 10, 2018

Answer:

Spring will compress by #"2.19 m"#

Explanation:

Kinetic energy of object = Energy stored in spring

#1/2mv^2 = 1/2kx^2#

From above equation

#x = vsqrt(m/k) = "2 m/s" × sqrt("6 kg"/("5 kg/s"^2)) = "2.19 m"#

Mar 10, 2018

Answer:

The compression is #=2.19m#

Explanation:

Mass of the object is #m=6kg#

Speed of the object is #v=2ms^-1#

The kinetic energy of the object is

#KE=1/2mv^2=1/2*6*(2)^2=12J#

This energy will be stored in the spring

#E=1/2kx^2#

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

Let the compression of the spring be #=xm#

Therefore,

#12=1/2*5*x^2#

#x^2=(24)/5=4.8m^2#

The compression of the spring is

#x=sqrt4.8=2.19m#