A 48 kg cart is moving across a frictionless floor at 3.3 m/s. A 50 kg boy, riding in the cart, jumps off the cart so that he hits the floor with zero velocity.
a.What is the velocity of the cart after the boy jumped?
b.What was the change in momentum of the boy?
c. What impulse did the boy receive?
d.What was the change in momentum of the cart?
e. What impulse did the cart receive?
a. Use conservation of momentum
(48 + 50)*3.3 = 48*Vfinal
Vfinal = 3.3*(98/48) = ___ m/s
b. The boy loses his initial momentum. The change is -50*3.3 = - ___ kg*m/s
c. Same answer as (b) (backwards)
d. Sama answer as (b) (but forwards)
e. Same answer as (b) (but forwards)
To answer these questions, we need to apply the principle of conservation of momentum. This principle states that the total momentum of a system remains constant if there are no external forces acting on it. In this case, the system consists of the cart and the boy.
a. To find the velocity of the cart after the boy jumps off, we can use the conservation of momentum equation:
(initial momentum of the system) = (final momentum of the system)
The initial momentum of the system is the momentum of the cart and the boy combined. The final momentum of the system is just the momentum of the cart after the boy jumps off. Since the problem states that the floor is frictionless, there are no external forces acting on the system, so momentum is conserved.
Initial momentum = (mass of cart + mass of boy) * initial velocity of system
Final momentum = mass of cart * final velocity of cart
Therefore:
(mass of cart + mass of boy) * initial velocity of system = mass of cart * final velocity of cart
Plugging in the values, we get:
(48 kg + 50 kg) * 3.3 m/s = 48 kg * final velocity of cart
Solving this equation gives us the final velocity of the cart after the boy jumps off.
b. The change in momentum of the boy can be calculated using the equation:
Change in momentum of boy = mass of boy * (final velocity of boy - initial velocity of boy)
Since the problem states that the boy hits the floor with zero velocity, the final velocity of the boy is 0 m/s. The initial velocity of the boy is the same as the initial velocity of the system. We can use this information to find the change in momentum of the boy.
c. The impulse received by the boy can be calculated using the equation:
Impulse = change in momentum of boy
d. The change in momentum of the cart can be calculated using the equation:
Change in momentum of cart = mass of cart * (final velocity of cart - initial velocity of cart)
e. The impulse received by the cart can be calculated using the equation:
Impulse = change in momentum of cart
By plugging in the appropriate values and using the equations above, we can find the answers to parts a, b, c, d, and e of the question.