Blocks A (mass 4.50 ) and B (mass 13.00 ) move on a frictionless, horizontal sur
ID: 1905306 • Letter: B
Question
Blocks A (mass 4.50 ) and B (mass 13.00 ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 7.00 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 A First : Find the maximum energy stored in the spring bumpers and the velocity of each block at that time. 1- Find the maximum energy ? 2- Find the velocity of A ? 3- Find the velocity of B ? Second : Find the velocity of each block after they have moved apart. 1- Find the velocity of A ? 2- Find the velocity of B ?Explanation / Answer
(1)
maximum energy will store when both object move with same velocity:
by conservation of momentum:
V*(4.5+13)=4.5*7
V = 1.8 m/s
maximum energy in bumper
E(max) = 0.5*4.5*7^2-0.5*17.5*1.8^2
= 81.9 J
(2)
the velocity of A = 1.8 m/s
(3)
the velocity of B = 1.8 m/s
(4)
Energy of mass A = 0.5*4.5*7^2 - 81.9
= 28.35 J
V(A) =- sqrt(2*28.35/4.5)
=-3.549 m/s
(5)
Energy of mass B = 81.9 J
V(B) =- sqrt(2*81.9/13)
= 3.549 m/s