Blocks A (mass 6.00 kg ) and B (mass 13.00 kg , to the right of A) move on a fri
ID: 1457678 • Letter: B
Question
Blocks A (mass 6.00 kg ) and B (mass 13.00 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.
Part A Find the maximum energy stored in the spring bumpers.
Part B Find the velocity of block A when the energy stored in the spring bumpers is maximum. Express your answer with the appropriate units.
Part C Find the velocity of block B when the energy stored in the spring bumpers is maximum. Express your answer with the appropriate units.
Part D Find the velocity of block A after the blocks have moved apart. Express your answer with the appropriate units.
Part E Find the velocity of block B after the blocks have moved apart. Express your answer with the appropriate units.
Explanation / Answer
mass of the block A is mA=6kg, velocity VA=2 m/sec
mass of the block B is mB=13kg, velocity vB=0.5 m/sec
A)
by using conservation of momentum,
mA*vA+mB*vB=(mA+mB)*V
6*2-13*0.5=(6+13)*v
===> final speed v=0.29 m/sec^2
now,
intial kinetic energy K1=1/2*mA*vA^2+1/2*mB*vB^2
K1=1/2*6*2^2+1/2*13*0.5^2
K1=13.625 J
final kinetic energy K2=1/2*(mA+mB)*v^2
K2=1/2*(6+13)*0.29^2
K2=0.8 j
enegry stored U=K1-K2
U=13.625-0.8
U=12.825 J
B)
when the energy stored in the spring is maximum,
velocity of block A is V=0.29 m/sec
C)
when the energy stored in the spring is maximum,
velocity of block B is V=0.29 m/sec
D)
let,
after collison
velocity of block A is u
velocity of block B is v
by using conservation of momentum,
mA*vA+mB*vB=mA*u+mB*v
6*2-13*0.5=6*u-13*v -----(1)
and their ralative velocity is,
VA-VB=v-u
2-0.5=v-u ------(2)
from equation no 1 and 2
u=-2.07 m/sec
v=-3.57 m/sec
velocity of block A is u=-2.07 m/sec
E)
velocity of block B is V=-3.57 m/sec