A spring with a constant of #3 (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 #8 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Aug 25, 2017

Answer:

#11.3cm(1dp)#

Explanation:

We need the following formulae

Elastic potential energy for springs

#EPE=1/2kx^2#

where#k= "the spring constant; "#

#x="the compression/extension of the spring"#

Kinetic energy

#KE=1/2mv^2#

#m="the mass of the object;" #

# v="the speed of the object"#

we have an object of mass#" "6kg" "#moving with speed #8ms^(-1)#

it will have kinetic energy of

#KE=1/2mv^2=1/2xx6xx8^2#

#KE=192J#

on collision with the spring all this will be given to the spring in terms of EPE

#KE=EPE#

#192=1/2xx3xxx^2#

#x^2=(2xx192)/3=128#

#:.x=sqrt(128)=11.3cm(1dp)#