Momentum and Impulse Chapter 7. Momentum Moving objects also resist acceleration. Massive objects in...

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Momentum and Impulse Chapter 7

Transcript of Momentum and Impulse Chapter 7. Momentum Moving objects also resist acceleration. Massive objects in...

Momentum and Impulse

Chapter 7

Momentum• Moving objects also resist

acceleration.• Massive objects in motion are more

difficult to accelerate than light objects

• A measure of the inertia of a moving object is called its momentum.

• Momentum has both magnitude and direction and is a vector quantity.

• Momentum is inertia in motion; the product of mass and velocity

velocity mass Momentum

Impulse• If the object does not break apart, the

momentum of an object changes only when its velocity changes, i.e. when it accelerates.

• For it to accelerate, an object must experience a net force.

• The longer time that a net force is applied, the greater is the change in momentum of an object.

• The resulting change in momentum is called impulse. Impulse is the product of net force and the time interval over which the force acts.

interval time forcenet

impulsemomentumin Change

Successful boxers understand impulse!• A boxer being punched receives the same impulse

whether his head moves into the punch or away from it.

• If his head is moving away from the punch, the time interval over which the force acts is extended and the force he experiences is smaller.

Impulse and Change in Momentum• Rock climbers also rely on extend time to

lessen the force when they fall. Their ropes are made of nylon or similar material because of its ability to stretch. If the rope is capable of stretching upon being pulled taut by the falling climber's mass, then it will apply a force upon the climber over a longer time period.

• When an object bounces it experiences a greater change in momentum and therefore a greater impulse. If the time interval is the same in each case, the force will be greater if the object bounces

Conservation of Momentum and Recoil• A change in momentum requires a net external force.• If no net external force acts, the momentum of a system

cannot change.

• When a rifle is fired, the system is initially at rest and only internal forces act on the system.

Law of conservation of momentumLaw of conservation of momentum: If there is no : If there is no external force, external force, initial momentum = final momentum

• Since the initial momentum is zero, the total final momentum zero must be zero so the rifle recoils with a momentum equal to and in the opposite direction to that of the speeding bullet.

Conservation of Momentum and Collisions• Momentum is always conserved in collisions

collisionafter momentum Total collision before momentum Total • If two pool balls of equal

mass collide, the first one initially moving and the second one initially at rest, after the collision, the first one will stop and the second will go with away with a velocity equal to the first ball’s initial velocity.

• Velocities exchange in this type of collision.

v1 = 5 m/sv2 = 0 m/s

v1 = 0 m/s

v2 = 5 m/s

m1 = m2 = 2 Kg

m1

m2 (2 kg)(5 m/s) + (2 kg)(0 m/s) = 10 Kg m/s

Total momentum before = 10 Kg m/s

(2 kg)(0 m/s) + (2 kg)(5 m/s) = 10 Kg m/sTotal momentum after= 10 Kg m/s

Conservation of Momentum and Collisions• When two objects of equal mass and traveling at

equal velocities in the opposite direction collide and bounce, they reverse direction and go in opposite direction at their initial speed

5 m/s 5 m/s

5 m/s 5 m/s

m1 = m2 = 2 Kg

(2 kg)(5 m/s) + (2 kg)(-5 m/s) = 0 Kg m/s

(2 kg)(-5 m/s) + (2 kg)(5 m/s) = 0 Kg m/s

collisionafter momentum Total collision before momentum Total

Total momentum before = 0 Kg m/s

Total momentum after= 0 Kg m/s

Conservation of Momentum and Collisions• If two pool balls of equal

mass collide, the first one initially moving quickly and the second one initially slowly, after the collision, the first one will move slowly and the second will move quickly with a velocity equal to the first ball’s initial velocity.

• Velocities exchange in this type of collision.

v1 = 5 m/sv2 = 1 m/s

v1 = 1 m/s

v2 = 5 m/s

m1 = m2 = 2 Kg

m1

m2 (2 kg)(5 m/s) + (2 kg)(1 m/s) = 12 Kg m/s

Total momentum before = 12 Kg m/s

(2 kg)(1 m/s) + (2 kg)(5 m/s) = 12 Kg m/sTotal momentum after= 12 Kg m/s

Conservation of Momentum and “Sticking” Collisions

• http://www.physicsclassroom.com/mmedia/momentum/fca.html

• What happens to the speed of the big fish after he swallows the little fish?

• http://www.physicsclassroom.com/mmedia/momentum/dft.html

Conservation of Momentum and increasing mass

• As the mass of the cart increases, its velocity must decrease so that the total momentum can remain constant. http://www.physicsclassroom.com/mmedia/momentum/cbb.html

BeforeCollisionMomentum

AfterCollisionMomentum

Change inMomentum

Dropped Brick 0 units 14 units +14 units

Loaded Cart 45 units 31 units -14 units

Total 45 units 45 units

Momentum and Impulse Questions1) What is the momentum of an object that is not moving?

2) Which has the greater momentum and which is harder to stop? A bullet with a mass of 10 g travels at 3000 m/s. A car with a mass of 1000 kg rolls at 3 cm/s. Explain or justify with a calculation.

3) Compare the change in momentum and impulse for an egg dropped 2 m on to concrete and an egg dropped 2 m onto foam. How does the force compare?

4) A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck.

5) If a 5-kg object experiences a 10-N force for a duration of 0.1-second, then what is the momentum change of the object?

Momentum and Impulse Answers1) The momentum of a object that is not moving is zero because

momentum is the product of mass and velocity, if the velocity is zero, the momentum is also zero.

2) 10 g = 0.01 kg so the momentum of the bullet is (0.01 kg)(3000 m/s) = 30 Kg m/s; 3 cm/s = 0.03 m/s so the momentum of the car is (1000 kg)(0.03 m/s) = 30 kg m/s. It is the same.

3) The change in momentum is the same because the egg goes from the speed it reaches after dropping 2 m to a stop in both cases. The impulse is also the same because impulse equal change in momentum. The force for the egg in the foam is less because it takes more time to stop in foam. Longer stopping time means less force.

4) (80 N)(0.1s) = 8 Ns5) (10 N)(0.1s) = 1 Ns, since impulse equals change in momentum, if

we know the impulse, we know the change in momentum

Momentum and Collision Questions1) A 1 Kg block1 initially traveling at 3 m/s on a frictionless surface

collides with a 1 Kg block2 at rest. Find a) the total momentum before the collision b) the total momentum after the collision c) the velocity of each block after the collision.

2) A 1 Kg block1 initially traveling at 3 m/s on a frictionless surface collides with a 1 Kg block2 traveling at 2 m/s. Find a) the total momentum before the collision b) the total momentum after the collision c) the velocity of each block after the collision.

3) A 1 Kg block1 initially traveling at 3 m/s East on a frictionless surface collides with a 1 Kg block2 at 3 m/s West. Find a) the total momentum before the collision b) the total momentum after the collision c) the velocity of each block after the collision.

4) A wagon is rolling down the sidewalk at 4 m/s in the rain. What will happen to the speed of the wagon as it fills with water? Explain.

Momentum and Collision Answers1) before: (1 kg)(3 m/s) + (1 kg)(0 m/s) = 3 Kg m/s after: (1 kg)

(0 m/s) + (1 kg)(3 m/s) = 3 Kg m/s; block 1: 0 m/s block 2: 3 m/s

2) before: (1 kg)(3 m/s) + (1 kg)(2 m/s) = 5 Kg m/s after: (1 kg)(2 m/s) + (1 kg)(3 m/s) = 5 Kg m/s; block 1: 2 m/s block 2: 3 m/s

3) before: (1 kg)(3 m/s) + (1 kg)(-3 m/s) = 0 Kg m/s after: (1 kg)(-3 m/s) + (1 kg)(3 m/s) = 0 Kg m/s; block 1: 3 m/s W block 2: 3 m/s E

4) The wagon will slow down as it fills with water because the mass of the wagon will increase as it fills with water. If momentum is conserved (remains constant), the velocity must decrease as the mass increases. For example, before: (10 kg)(4m/s) = 40 Kg m/s after: (20 kg)(2 m/s) = 40 Kg m/s

More Momentum Questions

Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

Strictly speaking, when a gun is fired, compared with the momentum of the recoiling gun, the opposite momentum of the bullet is

1. less.2. more.3. the same.

2 – acceleration depends on mass3 – the momentum is the same (but in the opposite direction )but the velocity for the bullet is much greater because its mass is less

Sources

• Conceptual Physics by Paul Hewitt• www.physicsclassroom.com• http://rigel.physics.unr.edu/faculty/phaneuf/c

lassinfo/index100.html