Blocks A (mass 7.00 kg ) and B (mass 11.00 kg , to the right of A) move on a fri
ID: 1446371 • Letter: B
Question
Blocks A (mass 7.00 kg ) and B (mass 11.00 kg , to the right of A) move on a frictionless, horizontal surface. Initially, block B is moving to the left at 0.500 m/s and block A is moving to the right at 2.00 m/s. The blocks are equipped with ideal spring bumpers. The collision is headon, so all motion before and after it is along a straight line. Let +x be the direction of the initial motion of A. A)Find the maximum energy stored in the spring bumpers. B) Find the velocity of block A when the energy stored in the spring bumpers is maximum. C)Find the velocity of block B when the energy stored in the spring bumpers is maximum. D)Find the velocity of block A after the blocks have moved apart. E)Find the velocity of block B after the blocks have moved apart.
Explanation / Answer
from the conservation of momentum
P_in = P_f
m1v1 = (m1+ m2) vcm
v cm = m1v1 /(m1+ m2)
= 7(2)/ 7+ 11)
=0.77 m/s
from the conservation of energy
U = K1- K2
= 1/2 m1 v1^2 - 1/2 ( m1+ m2) vcm^2
= 1/2 ( 7) (2))^2 - 1/2 ( 7+11) ) (0.77 )^2
=8.6639 J
(b)
the velocity of block A when the energy stored in the spring bumpers is maximum is 0.77 m/s
(c)
the velocity of block B when the energy stored in the spring bumpers is maximum is 0.77 m/s
(d)
the velocity of block A after the blocks have moved apart is
vA = ( m1- m2/ m1+ m2) v1
= 7-11/ 7+11 ( 2 m/s)
=-0.44 m/s
(e)
vB = 2 m1 v1/ m1+ m2 = 2( 7) (2)/ 7+ 11 = 1.55 m/s