Momentum is a

Momentum vectors

Impulse

Defined as a

Impulse is

Impulse is

Example

b) Determine the net impulse acting on the ball.

c) Determine the size of average force of the ball acting on the floor if the bounce lasts just 0.010 seconds.

a) Determine the change in momentum of the ball between the time right before it reaches the floor and just after it leaves the floor . 

A rubber ball of mass 50.0 grams is dropped above the floor a distance of 1.27m. It bounces back where it leaves the floor with a speed of 4.5m/s. 

Bus hits bug!

Elastic Cord vs a Steel Wire for block on frictionless surface

Both the cord & wire are equal in length relaxed. The blocks are given a push, sending them sliding towards the right.

Elastic

Steel

Force-time graph

A 5.0kg mass as subject to the following forces shown in the graph

Question

Two balls of equal mass roll towards a wall at identical speeds.  One ball, made of rubber, bounces off the wall at the same speed.  The other ball, made of clay, sticks to wall.  Which ball receives the greater impulse?  Why?

Question

A pitcher, starting from rest, winds up and throws 90mph fastball to catcher who stops the ball in his glove. Assume no friction or loss of energy.

1) Where does ball undergo a greater impulse?

2) Where does ball undergo a greater change in momentum?

3) Where does ball receive the greater force?

Center of Mass (COM)

COM is a point where you could consider all of the mass to be located or the average position of all of the particles (assuming identical particles) of an object.

COM doesn’t have to be geometric center

COM is also referred to as center of gravity (CG) which is a point where all of the weight of an object could be considered to be located.COM of object is what follows trajectory during projectile motion.

C.O.M. acts like mass of system…it can have vcom and acom

Position of C.O.M. remains constant throughout problemassuming no friction. Xcm initial = Xcm final

Stability

Stability has to do with location of CG in relation to base of support.

Lower CG is more stable

Placing a pivot at the CG

C.O.M. equation

Example

Three particles each of mass 2.5kg are located at the corners of a right triangle whose sides are 2.0m and 1.5m long. Locate the center of mass of the system.

1.5m

2.0m

Law of Conservation of Momentum

3 types of collisions

• ELASTIC

• INELASTIC

• PEFRECTLY INELASTIC

‘p’ conservation equations

ExampleBall A, mass 5.0 g, moves at a velocity of 20.0 cm/s, west.  It collides with Ball B, mass 10.0 g, moving east velocity 15.0 cm/s, 180.0°.  After the collision, ball A moves with a velocity of 8.0 cm/s, east.  Find the resulting velocity of ball B. 

A railroad car with mass of 5.0x105 kg collides with a stationary railroad car of equal mass.  After the collision, the two cars lock together and move off at 4.0m/s. a) Determine the initial speed of the first car.  b) Determine the % of KE lost due to the collision.

Example

A kid uses a pellet gun to fire a 1.0g pellet into a 15g can that initially rests atop a fence post.  The pellet is fired with a velocity of 30 m/s, east.  If the fence post is 1.5m above the ground, determine how far from the base the can will land assuming the pellet bounces off the can with velocity 5.0 m/s, west.

Example

Ballastic Pendulum

In a ballistics lab, a 10-gram bullet is shot into a 2-kg block of wood suspended by a 1-meter rope from the ceiling. During the collision, the bullet is embedded in the block and where the block makes a 53o angle with vertical.

a) Find the height the combo rises to after the collisionb) Find the speed of the combo after the collisionc) Find the speed of the bullet prior to collision

Collision in 2D

Conservation of momentum applies to all dimensions.

Momentum in x-direction must stay the same before and after collision. Same is true for y-direction.

A car with mass 950kg and speed 16m/s is moving east. A 1300kg truck is moving north at 21m/s. The car and truck collide at the middle of an intersection. They stick together. Find the speed and direction of the wreckage immediately following the collision. Neglect external forces.

2D Example

Example

a) remain the sameb) increase at a variable ratec) increase at a constant rated) decrease at a constant ratee) decrease at a variable rate

A cart loaded with sand slides along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the bottom of the cart. The speed of the cart will: