Mass 1 is a 15.0 g marble sliding to the left with a velocity of magnitude 0.72
ID: 2243894 • Letter: M
Question
Mass 1 is a 15.0 g marble sliding to the left with a velocity of magnitude 0.72 m/s on the frictionless, horizontal surface of an icy New York sidewalk and has a head-on, elastic collision with a larger 55 g (Mass 2) marble sliding to the right with a velocity of magnitude 0.44 m/s.
1) Calculate the momentum of the marbles before the collision.
2) Calculate the momentum of the marbles after the collision in terms of their final speeds.
3) Calculate the speed of Mass 1 after the collision.
4) Calculate the speed of Mass 2 after the collision.
5) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision).
Explanation / Answer
m1 = 0.015 kg, u1 = -0.72 m/s
m2 = 0.055 kg, u2 = 0.44 m/s
1)
Pi = m1*u1 + m2*u2 = 0.015*(-0.72)+0.055*0.44 = 0.0134 kg.m/s ( to wards right)
2)
Pf = m1*v1 + m2*v2 = 0.0134 kg.m/s (towards right)
3)
v1 = (m1-m2)*u1/(m1+m2) + 2*m2*u2/(m1+m2) = 1.103 m/s (towards right)
4)
v1 = (m2-m1)*u2/(m1+m2) + 2*m1*u1/(m1+m2) = -0.057 m/s (towards left)
5)
Ki - Kf = (0.5*m*u1^2+0.5*m2*u2^2) - (0.5*m1*v1^2 + 0.5*m2*v2^2) = 0