An engine of the orbital maneuvering system (OMS) on a space shuttle exerts a force of 30000 N j for 4.00 s, exhausting a negligible mass of fuel relative to the 95,000 kg mass of the shuttle.
(a) What is the impulse of the force for this 4.00 s?
(b) What is the shuttle's change in momentum from this impulse?
(c) What is the shuttle's change in velocity from this impulse?
(d) Why can't we find the resulting change in kinetic energy of the shuttle?

Answer to Example Impulse Problems

a. Impulse = Ft = 30000(4) = 120000 N-s

b. change in momentum = impulse = 120000 N-s

c. j = m∆v

120000 = (95000)∆v

∆v = 1.26 m/s

d. We do not know the initial velocity.

Impulse Problems

1. A particle with momentum mv₁ experiences a force which leaves it with momentum mv₂. Draw an arrow to represent the impulse the particle experienced.
Impulse, a vector quantity, can be determined from the difference between the momentum vectors diagrammed here.

2. A 1000 kg car accidentally drops from a crane and crashes at 30 m/s to the ground below and comes to an abrupt halt. What impulse acts on the car when it crashes?

3. If a force of 300N is exerted upon a 60 kg mass for 4 seconds, how much impulse does the mass experience?

4. Two pucks with identical mass are traveling on a frictionless surface at right angles to each other with velocities v₁ and v₂ respectively (v₁ = 2v₂). The pucks collide and stick together.

a. Draw momentum vectors for both pucks before the collision.
b. Draw the momentum vector for the combined body immediately after the collision.
c. What is the impulse of the system?

5. A billiard ball approaches a cushioned edge of a billiard table with momentum, p. After the collision with the cushion, it bounces straight back with the same amount of momentum in the opposite direction. What is the impulse on the ball?

6. A bullet, of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30-degrees with a plane of the plate. It ricochets off at the same angle, at a speed of 320 m/s. What is the magnitude of the impulse that the wall gives to the bullet?

7. A bungee jumper (m = 77.00 kg) tied to a 32.00 m cord, leaps off a 62.00 m tall bridge. He falls to 9.00 m above the water before the bungee cord pulls him back up. What size impulse is exerted on the bungee jumper while the cord stretches.

8. While waiting in his car at a stoplight, an 80-kg man and his car are suddenly accelerated to a speed of 5 m/s as a result of a rear-end collision. Assuming the time taken to be 0.3s, find the
a) impulse on the man and

b) the average force exerted on him by the back seat of his car

9. The momentum of a 30.0-g sparrow with a speed of 12 m/s is 0.36 kg*m/s. What will be its momentum 12s later if a constant .02 N force due to air resistance acts on it?

10. Two carts one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?

11. During the service of a professional tennis player the racket exerted an average force of 152.0 N on the ball. If the ball has a mass of 0.070 kg and was in contact with the strings of the racket for 0.030 s, what was the kinetic energy of the ball as it left the racket? Assume that the ball started from rest. Assume that air resistance was negligible.

ANSWERS

Solutions to selected questions are below.

For solutions to all the problems on this page click here.

1. j = mv₂ - mv₁ = mv₂ + (-mv₁)

The impulse vector is drawn from the head of one momentum vector to the head of the other.

j = mΔv assuming constant mass.

j = 1000(-30) = -30 000 kg-m /s

The impulse is 30000 kg-m/s upwards.

For solutions to all the problems on this page click here.