Chapter 6: Momentum & Collisions

Impulse-Momentum Theorem

--> Impulse = net force (time interval) = change in momentum

Perfectly inelastic collisions

--> momentum is conserved, but kinetic energy is not conserved --> objects STICK together during collisions, so their final velocities are the same --> Vf can be found using pi = pf ~ (m1v1)i + (m1v1)f = Vf (m1 + m2)

Inelastic collisions

--> momentum is conserved, but kinetic energy is not conserved --> pi = pf --> objects BOUNCE

a ball with a momentum of 4 kg (m/s) hits a wall and bounces straight back without losing any kinetic energy. What is the change in the ball's momentum? a. -8 kg (m/s) b. -4 kg (m/s) c. 0 kg (m/s) d. 8 kg (m/s)

-8 kg (m/s) work: pf -pi --> -4 - (+4) = -8

How to Solve One Dimensional Collision Problems

1. choose coordinate axis that is in the direction of motion 2. draw a diagram of the 2 objects and label the velocity, and total mass 3. write the conservation of momentum equation of BEFORE and AFTER the collision and fill in the values 4. With an elastic collision: do the same 5. Solve with a system of equations

a 0.2 kg baseball is pitched with a velocity of 40 m/s and is then batted to the pitcher with a velocity of 60 m/s. What is the magnitude of change in the ball's momentum? a. 2 kg (m/s) b. 4 kg (m/s) c. 8 kg (m/s) d. 20 kg (m/s)

20 kg (m/s) work: 0.2(40) + 0.2(60) = 20

which of the following statements properly relates the variables in the equation F (change in time) = change in p? a. a large constant force change an object's momentum over a long time interval b. a large constant force acting over a long time interval causes a large change in momentum c. a large constant force changes an object's momentum over a long time interval

a large constant force acting over a long time interval causes a large change in momentum

In order to change the momentum of an object, you need

a net force --> Net force = change in momentum / time interval

Recoil

a phenomenon with the action, reaction, and the exchange of momentum between 2 objects; movement backwards, usually from some force or impact --> firing a gun or shooting an arrow

if a force is exerted on an object, which of the following is true? a. a large force always produces a large change in the object's momentum b. a large force produces a large change in the object's momentum only if the force is applied over a very short time interval c. a small force applied over a long time interval can produce a large change in the object's momentum

a small force applied over a long time interval can produce a large change in the object's momentum

which of the following situations is an example of a significant change in momentum? a. a tennis ball is hit into a net b. a helium filled balloon rises upwards into the sky c. an airplane flies into some scattered white clouds d. a bicyclist rides over a leaf on the pavement

a tennis ball is hit into a net

Elastic collisions

both momentum and kinetic energy is conserved --> (v1 - v2)i = - (v1 - v2)f

Impulse

changing an objects momentum requires a continuous force over a period of time interval --> net force (time interval) --> change in momentum --> kg (m)/ s

a 20 kg shopping cart moving at a velocity of 0.5 m/s collides with a store wall and stops. The momentum OF THE SHOPPING CART a. increases b. decreases c. remains the same d. is conserved

decreases

two objects move separately after colliding, and both the total momentum and total kinetic energy remain constant. Identify the type of collision a. elastic b. nearly elastic c. inelastic d. perfectly inelastic

elastic

True or false: impulse is a scalar quantity

false --> impulse is a vector quantity with the same direction as the constant force acting on the object

a roller coaster climbs up a hill at 4 m/s and then sips down the hill at 30 m/s. The momentum of the roller coaster a. is greater up the hill than down the hill b. is greater down the hill than up the hill c. remains the same throughout the ride d. is zero throughout the ride

is greater down the hill than up the hill

a billiard ball collides with a stationary identical billiard ball in an elastic hard-on collision. After the collision, which of the following is true of the first ball? a. it maintains its initial velocity b. it has 1/2 its initial velocity c. it comes to rest d. it moves in the opposite direction

it comes to rest

Linear Momentum (p)

mass (velocity) --> kg (m)/ s

the impulse experienced by a body is equivalent to the body's change in a. velocity b. kinetic energy c. momentum d. force

momentum

In a two-body collision a. momentum is always conserved b. kinetic energy is always conserved c. both momentum and kinetic energy are always conserved

momentum is always conserved

a rubber ball moving at a speed of 5 m/s hit a flat wall and returned to the thrower at 5 m/s. The magnitude of the momentum of the rubber ball a. increase b. remained the same c. was not conserved d., decreased

remained the same

a soccer ball collides with another soccer ball at rest. The total momentum of the balls a. is zero b. increases c. remains constant d. decreases

remains constant

a child with a mass of 23 kg rides a bike with a mass of 5.5 kg at a velocity of 4.5 m/s to the south. Compare the momentum of the child with the momentum of the bike. a. both the child and the bike have the same momentum b. the bike has a greater momentum than the child c. the child has a greater momentum than the bike

the child has a greater momentum than the bike --> same velocity --> the child has a greater mass than the bike

Average force

the constant force delivering the same impulse to the object as the actual time varying force

when comparing the momentum of two moving objects, which of the following is correct? a. the object with the higher velocity will have less momentum if the masses are equal b. the more massive object will have less momentum if its velocity is greater c. the less massive object will have less momentum if the velocities are the same d. the more massive object will have less momentum if the velocities are the same

the less massive object will have less momentum if the velocities are the same

the change in an object's momentum is equal to a. the product of the mass of the object and the time interval b. the product of the force applied to the object and the time interval c. the time interval divided by the net external force d. the net external force divided by the time interval

the product of the force applied to the object and the time interval

the law if conservation of momentum states that a. the total initial momentum of all objects interacting with one another usually equals the total final momentum b. the total momentum of all objects interacting with another is zero c. the total momentum of all objects interacting with another remains constant regardless of the nature of the forces between the objects

the total momentum of all objects interacting with another remains constant regardless of the nature of the forces between the objects

two skaters stand facing each other. One skater's mass is 60 kg, and the other's mass is 72 kg. If the skaters push away from each other without spinning, a. the lighter skater has less momentum b. their momenta are equal but opposite c. their total momentum doubles

their momenta are equal but opposite

two swimmers relax close together on air mattresses in pool. One swimmer's mass is 48 kg, and the other's mass is 55 kg. If the swimmers push away from each other, a. their total momentum triples b. their momentum decreases c. their momenta are equal but opposite

their momenta are equal but opposite

True or False: momentum is a vector quantity

true

True or false: momentum of an object is conserved when the net force is zero

true

a person sitting in a chair with wheels stands up, causing the chair to roll backwards across the floor. The momentum of the chair a. was zero while stationary and increased when the person stood b. was greater while the person sat in the chair c. remained the same d. was zero when the person got out of the chair and increased while the person sat

was zero while stationary and increased when the person stood

Conservation of Momentum

when no net external force acts on a system, the total momentum of the system remains constant in time (/conserved) --> pi = pf --> must be an isolated system

Glancing collisions

x-component : (m1v1)i + 0 = (m1v1)f(cos theta) + (m2v2)f(cos beta) y-component : 0 + 0 = (m1v1)f(sin theta) + (m2v2)f(sin beta)