AP Physics I.D

Impulse and Momentum

7.1 Impulse-Momentum Theorem

Momentum

• Product of mass and velocity

• It’s a vector Victor

Impulse (a vector and has same direction as average force)

Examples of impulse

Ex. A golf ball with a mass of 0.050 kg is hit from a tee. The velocity of the ball off the tee is 44 m/s. What is the a) impulse for the ball and b) the average force if the time the club is in contact with the ball is 9.1 EE – 4 s?

Ex. In a crash test, a 1.50 EE 3 kg car collides with a wall with a speed of 15.0 m/s. The car bounces back from the wall with a speed of 2.60 m/s. The car is in contact with the wall for 0.150 s. Find the average force exerted on the car by the wall.

p. 206: 3-5, 9, 12-14

4. 4.24 kg·m/s

12. 320 kg·m/s at 16º N of E

14. 344 N (find v and use impulse formula)

7.2 Conservation of Linear Momentum

Two billiard balls on a Physicstown (frictionless) table

Two types of forces on the system

• Internal – forces that objects within the system exert on each other

• External – forces that objects outside the system exert on each other

A derivation from Newton’s Third Law

Linear momentum is conserved if the sum of the external forces is zero (the momentum before

the collision is equal to the momentum after the collision)

Ex. A Ford Excursion at rest with a mass of 1.80 EE 3 kg is struck in the rear by a Ford Pinto with a mass of 9.0 EE 2 kg. The cars become entangled and move in the initial direction of the Pinto. What is the final velocity of the entangled cars if the initial velocity of the Pinto is 20.0 m/s?

Rifle Recoil: Find the recoil velocity of a 5.0 kg rifle that shootsa 0.050 kg bullet at a speed of 120 m/s.

p. 207: 15-16, 18, 20, 24; Rev. p. 123: 40, 43

16. 7.1 EE 5 m/s

18. 96 kg

20. 1.5 m

24. 2.2

40. a) 550 N b) 7.2 m/s

7.3 Collisions in One Dimension

Elastic collision – momentum and kinetic energy are conserved

(objects bounce off one another – in real life this only happens at the

atomic level)

Inelastic collision – momentum is conserved, but kinetic energy is

not

Completely inelastic collision – all kinetic energy converted to

other forms of energy – the objects stick together (thud)

Note: momentum is conserved if no external forces act on the system, but kinetic energy is conserved only in

elastic collisions.

Ex. A bullet with a mass of 0.0100 kg strikes, and is embedded in a block (mass of 2.50 kg) that is suspended by a thin cord. The block rises a vertical height of 0.650 m because of the collision. What is the initial velocity of the bullet assuming the collision is elastic?

7.4 Collision in Two Dimensions

If no external forces act on a system, horizontal and vertical components of

momentum are conserved.

Ex. A ball moving with a speed of 3.0 m/s along the positive x-axis strikes a second ball with twice the mass initially at rest. The first ball glances off the second and moves off at angle above the x-axis while the second moves at an angle of 35º below the x-axis at 1.0 m/s. Find the angle and speed of the first ball after the collision.

84B2, 85B1, 01B2

84B2 – not hard. You complete

85B1

a) 1.5 m/s

b) 667/1

c) 0.11 m

01B2

a) 0.42 m/s

b) Use the usual kinematics (0.21 m)

c) 0.30 m/s

d) 0.015 kg·m/s