Question

Blocks A (mass 5.00 kg ) and B (mass 9.00 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.

Answer 1

(a) maximum energy stored in spring bumpers equals the kinetic energy of block-A before collision

maximum energy stored in spring bumpers = (1/2) m v² = (1/2) 5 4 = 10 J

(b) zero. when maximum energy is stored in spring bumper, block-A has lost all its initial kinetic energy

(c) zero. when maximum energy is stored in spring bumper, block-B has not gain any kinetic energy

(d) Let us assume half of initial kinetic energy i.e., 5 J stored in each spring.

Energy stored in spring attached to block-B is transferred to block-A .

Hence block-A moves with energy 5 J, its speed is given by, (1/2)mv² = 5 J

or v = ( 10 / m )^1/2 = ( 10 / 5 )^1/2 = 1.414 m

(e) Energy stored in spring attached to block-A is transferred to block-B

Hence block-B moves with energy 5 J, its speed is given by, (1/2)mv² = 5 J

or v = ( 10 / m )^1/2 = ( 10 / 9 )^1/2 = 1.054 m