Blocks A (mass 4.50 kg ) and B (mass 7.50 kg ) move on a frictionless, horizonta
ID: 1434320 • Letter: B
Question
Blocks A (mass 4.50 kg ) and B (mass 7.50 kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 2.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of block 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 they have moved apart E) Find the velocity of B after they have moved apart.
Explanation / Answer
A) Stored spring energy will be maximum when they are moving with same velocity.
so using momentum conservation,
4.50 x 2 + 7.50 x 0 = 4.50v + 7.50v
v = 0.75 m/s
difference of energy will be stored in spring.
spring energy = initial KE - final KE
= [ 4.50 x 2^2 / 2 ] - [ (4.50 + 7.50) x 0.75^2 / 2 ]
= 5.625 J
b) velocity of block A = 0.75 m/s
c) velocity of block B = 0.75 m/s
d) after they moved apart suppose A move with vA in opposite direction and B with vB in same direction
for elastic collision.
2 = vA + vB
vB = 2 - vA
Using momentum conservation,
4.50 x 2 = -4.50vA + 7.50vB
9 = -4.50vA + 7.50 ( 2 - vA)
9 - 15 = 12vA
vA = 0.5 m/s (in opposite direction or - 0.5 m/s)
E) vB = 2 - vA = 2 - 0.5 = 1.5 m/s