Download presentation

Presentation is loading. Please wait.

Published byRebecca Mifflin Modified over 3 years ago

1
Linear Momentum For an individual mass we define the linear momentum to be: From the 2 nd law we have: This is actually how Newton originally formulated the 2 nd law. The “ma” is a special case when m is not changing.

2
Linear Momentum of a System of Particles For a system of many particles, we can define the “total linear momentum”: Then we can write: The total linear momentum is a result of the total mass moving with the velocity of the CM

3
Let us differentiate the total momentum: If there are no external forces, then momentum is conserved: This is a vector equation. If there are not external forces in say the x-direction, then P xo = P xf even if there are external forces in the y-direction.

4
Elastic Collisions in 1-D Elastic means KE stays the same:

5
Dividing two equations gives (upon rearrangement): The relative velocity changes direction but keeps same magnitude. Only true in 1-D, elastic collisions. Example: Ping pong ball collides with stationary bowling ball. Multiply by M and subtract Bounces back with same speed

6
Example: Bowling ball hits stationary ping pong ball. Multiply by M and add Barry Bonds uses a light bat

7
A two dimensional collision

8
Example: a 4 kg mass heading in the – y direction at 12 m/s collides and sticks to a 6 kg mass moving in the + x direction at 10 m/s. Find the magnitude and direction of the final velocity.

9
Impulse For a constant force, let is define a vector quantity called impulse as the product of the force times the time over which it acts: In one dimension, we need only worry about the sign. If the force is not constant during the time over which the force acts, we define through an integral: Note the analogy to our definition of work. Of course a huge difference is work is a scalar and impulse is a vector. For any component, the impulse will be the area under the F i vs t graph.

10
So why bother with impulse? Suppose we focus on the impulse delivered by the net force.

11
Impulse – Momentum Theorem p = p f – p i = F dt tftf titi The impulse of the force F acting on a particle equals the change in the momentum of the particle. J = p

12
Example: A 0.1 kg mass moving with a speed of 10 m/s along the x-axis collides head on with a stationary 0.1kg mass. The magnitude of the force between the two is shown below as a function of time. Find the final speed and direction of each mass. For 2 nd block: For 1 st block: Impulse is negative by Newton’s 3 rd Law

Similar presentations

Presentation is loading. Please wait....

OK

Center of Mass and Linear Momentum

Center of Mass and Linear Momentum

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on computer malware scanner pro Ppt on sedimentary rocks formation Ppt on meaning of economics Ppt on art of war audio Ppt on electric meter testing school Ppt on 555 timer application Ppt on quality education quotes Ppt on linear programming in operations research Ppt on dry cell and wet cell Ppt on networking related topics in biology