A ball with a mass of #5 kg# moving at #3 m/s# hits a still ball with a mass of #8 kg#. If the first ball stops moving, how fast is the second ball moving?
1 Answer
Explanation:
We can calculate the final velocity of the second ball using momentum conservation. Momentum is conserved in all collisions.
In an inelastic collision, momentum is conserved as always, but energy is not; part of the kinetic energy is transformed into some other form of energy. Therefore, we have an inelastic collision.
#color(skyblue)(vecp=mvecv)# The equation for momentum, where
#m# is the mass of the object and#v# is the object's velocity.
Momentum conservation:
#DeltavecP=0#
#=>vecp_f=vecp_i#
For multiple objects, we use superposition as with forces:
#vecP=vecp_(t o t)=sumvecp=vecp_1+vecp_2+...+vecp_n#
So we have:
#=>color(crimson)(m_1v_(1i)+m_2v_(2i)=m_1v_(1f)+m_2v_(2f))#
We are given the following information:
#|->"m"_1=5"kg"# #|->"v"_(1i)=3"m"//"s"# #|->"v"_(1f)=0# #|->"m"_2=8"kg"# #|->"v"_(2i)=0#
Factoring in our zero values, we now have:
#m_1v_(1i)+cancel(m_2v_(2i))=cancel(m_1v_(1f))+m_2v_(2f)#
#=>m_1v_(1i)=m_2v_(2f)#
Which we can solve for
#color(darkgray)(v_(2f)=(m_1v_(1i))/m_2)#
Substituting in our known values:
#v_(2f)=((5"kg")(3"m"//"s"))/(8"kg")#
#=1.875"m"//"s"#
#~~color(darkblue)(2"m"//"s")#
This answer can be checked by comparing the momentum before and after the collision. They should both be equal by momentum conservation.
