Momentum and Newtons Laws

1
Momentum and Newtons Laws

• Section 5.4

2
Momentum aka the big Mo

• Newton first thought of the concept of a
  quantity of motion made up of mass and
  velocity. We call it momentum.
• pmv ( a vector quantity )
• A train moving slowly and a bullet moving quickly
  both have a lot of momentum

3
Some typical interactions involving momentum

• Collisions
• Explosions
• Recoil

4
Defining Momentum

• The product of an objects mass and its velocity.
  The direction of the momentum of an object is the
  same as the direction of its velocity.
• Since p mv, the units for momentum are kgm/s
• Example a 10.0 kg mass travelling E at 20.0
  m/s has a momentum of
• 200. kgm/s E

5
Defining Momentum

• Momentum is really a measure of the difficulty
  encountered in bringing an object to rest. The
  greater the mass or velocity of an object, the
  bigger its momentum.
• Momentum is a conserved quantity. Through
  repeated investigation, it has been determined
  that in a closed system, the total momentum
  before the interaction takes place equals the
  total momentum after the interaction. This is
  referred to as the Law of Conservation of Momentum

6
Practice Problems

• A fully loaded Redi-Mix cement truck has mass 42
  000 kg travels north at 70. km/h. a) Calculate
  its momentum.
• b) How fast must a Toyota Matrix of mass 1270 kg
  travel in order to have the same momentum as the
  truck?

7
Solution to problem

• a)
• p mv 70. km/h ?19.4 m/s
• p 42 000 kg 19.4 m/s
• p 814 800 kgm/s N
• p 8.1 x 105 kgm/s N
• b) p mv so
• v p/m 814 800 kgm/s /1270 kg
• v 642 m/s N ?640 m/s N

8
Practice Problems

• Saku Koivu has mass 90. kg skates towards Biron
  who has mass 100. kg. If Koivu is skating at 40.
  km/h, how much momentum does he have when he
  crashes into Biron? If they become entangled i.e.
  stick together, how fast do they travel?

9
Solution to practice problem

• p mv ? (90. kg)(11.111 m/s) 1.0 x 103 kgm/s
  (toward Biron)
• v p/(m1 m2) (999.999 kgm/s)/(190 kg)
• v 5.26 m/s ? 5.3 m/s ( in the original
  direction of motion)

10
Defining Impulse

• Originally, Newton thought that a force was
  needed to bring about a change in an object s
  motion i.e a force is required to produce a
  change in an objects momentum. Symbolically,
  this can be represented as
• F ?p/ ?t
• F m?v/ ?t
• F ma

11
Defining Impulse

• From the previous equation,
• F?t m?v
• The product of a force and the time interval over
  which it acts is called the impulse of the
  force. The symbol for impulse is J
• J F?t ( a vector quantity) units are Ns

12
The Impulse Momentum Theorem

• Because the impulse of a force causes the
  momentum of an object to change,
• F?t m?v and Ns kgm/s
• See text example p. 201

13
Impulse and Auto Safety

• Reducing forces during car crashes
• can sometimes save lives and reduce the
  severity of injuries. This can be accomplished by
  designing cars with crumple zones. While the
  front or back zone is crumpling, time is passing,
  energy is being dissipated and the impact on the
  passengers is reduced.
• Other features such as air bags also help. By
  increasing ?t, F is decreased.