Chapter 9: Linear Momentum & Collisions WICKED FACE PUNCH!!!

9.1 – Linear Momentum Linear momentum is defined as the product of an objects mass (m) and velocity (v). Units = kg·m/s Momentum is a vector, with it’s direction in the same direction as the velocity. Coffee?

Change in Momentum Initial pFinal p Beanie Baby Rubber Ball

Example 9.1

Riddle Me This… Consider the following objects: (1) an electron (m = 9.1 × 10  31 kg, v = 5.0 × 10 7 m/s) (2) the Hubble Space Telescope (m = 1.1 × 10 4 kg, v = 7.6 × 10 3 m/s) (3) a snail (m = 0.02 kg, v = m/s) (4) the largest super oil tanker (m = 1.5 × 10 8 kg, v = 2.0 m/s) (5) a falling rain drop (m = kg, v = 9.5 m/s) Which one of these objects requires the greatest change in momentum to stop moving? a) 1 b) 2 c) 3 d) 4 e) 5

ConcepTest 9.1 Rolling in the Rain a) speeds up b) maintains constant speed c) slows down d) stops immediately An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (Assume that the rain falls vertically into the box.)

Because the rain falls in vertically, it adds no momentum to the box, thus the box’s momentum is conserved. However, because the mass of the box slowly increases with the added rain, its velocity has to decrease. ConcepTest 9.1 Rolling in the Rain a) speeds up b) maintains constant speed c) slows down d) stops immediately An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (Assume that the rain falls vertically into the box.) Follow-up: What happens to the cart when it stops raining?

9.2 – Momentum & Newton’s Second Law Newton’s Second Law This version of Newton’s second law is only valid when objects have constant mass! General version of Newton’s Second Law

9.3 - ImpulseImpulse Elastic vs Inelastic Collisions Elastic Collision – Momentum is conserved. – Kinetic Energy is conserved. Inelastic Collision – Momentum is conserved. – Kinetic Energy is NOT conserved

9.3 - Impulse Impulse (I) is defined as the product of: – Average force (F av ) applied to an object. – Time duration (Δt) that force is being applied. Impulse is equal to the change in momentum. (Momentum-Impulse Theorem)

9.3 Impulse SI Units for Impulse N·s = kg·m/s Remember, Impulse is a vector!

9.3 - Impulse Therefore, the same change in momentum may be produced by a large force acting for a short time, or by a smaller force acting for a longer time.

9.3 - Impulse

Jumping For Joy

Given Information Our contestant has a mass of 72 kg. Jump results in an upward speed of 2.1 m/s. Requested Information (A)What is the impulse experienced by the contestant? (B)What additional average upward force does the floor exert if the contestant pushes down for 0.36 seconds during the jump?

9.4 – Conservation of Linear Momentum Linear Momentum is a conserved quantity. Formally: if the net force acting on an object is zero, its momentum is conserved.

Internal vs External Forces Internal Forces Act between objects within the system. Come in action-reaction pairs (aka Newton’s Second Law) Always sum to zero. May change the momenta of components within the system, but the system’s momentum does not change. External Forces May or may not sum to zero. Only an external force can change the moment of an object.

9.4 – Conservation of Linear Momentum An example of internal forces moving components of a system:

Example 9-3 (pg ) Given Information Person from canoe 1 pushes on canoe 2 with a force of 46 N. Mass of canoe 1 & occupants is 130 kg. Mass of canoe 2 & occupants is 250 kg. Requested Information Find the momentum of each canoe after 1.20 seconds of pushing.

9.5 – Inelastic Collisions Collision? – Two or more objects strike each other. – F ext is negligibly small. Inelastic Collisions – Momentum is conserved. – Kinetic Energy is NOT conserved. Completely Inelastic Collisions – Objects stick together after collision.

Inelastic Collision in 1-D BeforeAfter

Example 9-5 Find the height the pendulum rises in terms of variables.

Inelastic Collisions in 2-D Must conserve momentum component by component.

Example 9-6 Given Information – m 1 = 950 kg – v 1i = 16 m/s – m 2 = 1300 kg – v 2i = 21 m/s Requested Information – Find the speed and direction of vehicles just after collision. (Assume completely inelastic).

9.6 – Elastic Collisions In elastic collisions – Momentum is conserved – Kinetic Energy is conserved

Cons. Of MomentumCons. Of Kinetic Energy Recall… Momentum rewritten… Kinetic Energy rewritten…

Rearrange…

Example 9-7 Given Information – m 1 =.130 kg – v 1i = 1.11 m/s – m 2 =.160 kg – v 2i = 1.21 m/s – v 2f = 1.16 m/s – Θ = 42° Requested Information – v 1f = ? – Φ = ?

9.7 – Center of Mass Center of mass of a system is the point where the system can be balanced in a uniform gravitational field. “Average location of a system’s mass.”

9.7 – Center of Mass X cm for multiple objects… Y cm for multiple objects…

Motion of the Center of Mass Velocity of the Center of Mass Acceleration of the Center of Mass What is the result of a force acting on the center of mass? F net,ext = Ma cm