In: Physics
Two objects, A and B, are released from rest in free space (no other masses are near). Object A has a greater mass than object B. They accelerate toward each other under the action of their mutual gravitational attraction.
a. On which object is the greater work done?
b. At the instant just before they hit, which object will have the momentum with the greatest magnitude?
c. At the instant just before they hit, which object will have the greater kinetic energy? Explain.
in all of the above could you explain how you got to the answer.
Thank you so much!
PART A:
work done=force*displacement
now force on each object is same.
but displacement will be higher for the object which has higher acceleration i.e. less mass .(acceleration=force/mass)
hence work done will be higher for the object with less mass i..e object B.
part b:
as initially velocity of center of mass is 0, if velocity just before collision is Va and Vb respectively for object A and object B, then conserving momentum,
mass of A*Va+mass of B*Vb=0
==>Va=-mass of B*Vb/mass of A
as mass of A >mass of B,hence |Va| < |Vb|
but their momentum magnitude will be the same.
so both the objects will have same mmomentum
part c:
let mass of A is Ma and mass of B is Mb
then kinetic energy of A=0.5*Ma*Va^2
=0.5*Ma*(Mb*Vb/Ma)^2
=0.5*Mb^2*Vb^2/Ma=0.5*Mb*Vb^2*(mMb/Ma)
=kinetic energy of B*(mass of B/mass of A)
as mass of B < mass of A
mass of B/mass of A <1
hence kinetic energy of A < kinetic energy of B