(b) What will be the speed of the skier and child just after they collide?
(c) If the collision occurs in half a second, how much force will be experienced by each person?Solutions to Practice Problems
1 . B— Impulse is force times the time interval of collision, and is also equal to an object’s change in
momentum. Solving for force, F = Δp /Δt . Because the ball still has the same mass, and still changes
from speed v 0 to speed zero, the ball’s momentum change is the same, regardless of the collision time.
The collision time, in the denominator, doubled; so the entire expression for force was cut in half.
2 . E— Still use F = Δp /Δt , but this time it is the numerator that changes. The ball still is brought to rest
by the glove, and the mass of the ball is still the same; but the doubled velocity upon reaching the glove
doubles the momentum change. Thus, the force doubles.
3 . B— The total momentum after collision is zero. So the total momentum before collision must be zero
as well. The mass m moved 5 m/s to the right, giving it a momentum of 5m units; the right-hand mass
must have the same momentum to the left. It must be moving half as fast, 2.5 m/s, because its mass it
twice as big; then its momentum is (2m )(2.5) = 5m units to the left.
4 . C— Because the balls are identical, just pretend they each have mass 1 kg. Then the momentum
conservation tells us that
(1 kg)(+4 m/s) + (1 kg)(−3 m/s) = (2 kg)(v ′).
The combined mass, on the right of the equation above, is 2 kg; v ′ represents the speed of the
combined mass. Note the negative sign indicating the direction of the second ball’s velocity. Solving, v
′ = +0.5 m/s, or 0.5 m/s to the right.5 . (a) This part is not a momentum problem, it’s a Newton’s second law and kinematics problem. (Or it’s
an energy problem, if you’ve studied energy.) Break up forces on the skier into parallel and
perpendicular axes—the net force down the plane is mg (sin 45°). So by Newton’s second law, the
acceleration down the plane is g (sin 45°) = 7.1 m/s^2 . Using kinematics with intitial velocity zero
and distance 100 m, the skier is going 38 m/s (!).
(b) Now use momentum conservation. The total momentum before collision is (75 kg)(38 m/s) = 2850
kg·m/s. This must equal the total momentum after collision. The people stick together, with
combined mass 115 kg. So after collision, the velocity is 2850 kg·m/s divided by 115 kg, or about
25 m/s.
(c) Change in momentum is force multiplied by time interval ... the child goes from zero momentum to
(40 kg)(25 m/s) = 1000 kg·m/s of momentum. Divide this change in momentum by 0.5 seconds, and
you get 2000 N, or a bit less than a quarter ton of force. Ouch!
Rapid Review
• Momentum equals an object’s mass multiplied by its velocity. However, you can also think of
momentum as the amount of “oomph” a mass has in a collision.
• Impulse equals the change in an object’s momentum. It also equals the force exerted on an object
multiplied by the time it took to apply that force.