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

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.

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 momentum: If there is no 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 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. m1 = m2 = 2 Kg v1 = 5 m/s v2 = 0 m/s m1 m2 (2 kg)(5 m/s) + (2 kg)(0 m/s) = 10 Kg m/s Total momentum before = 10 Kg m/s v1 = 0 m/s v2 = 5 m/s (2 kg)(0 m/s) + (2 kg)(5 m/s) = 10 Kg m/s Total 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 m1 = m2 = 2 Kg (2 kg)(5 m/s) + (2 kg)(-5 m/s) = 0 Kg m/s Total momentum before = 0 Kg m/s 5 m/s 5 m/s (2 kg)(-5 m/s) + (2 kg)(5 m/s) = 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. m1 = m2 = 2 Kg v1 = 5 m/s v2 = 1 m/s m1 m2 (2 kg)(5 m/s) + (2 kg)(1 m/s) = 12 Kg m/s Total momentum before = 12 Kg m/s v1 = 1 m/s v2 = 5 m/s (2 kg)(1 m/s) + (2 kg)(5 m/s) = 12 Kg m/s Total 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 Before Collision Momentum After Collision Momentum Change in Momentum Dropped Brick 0 units 14 units +14 units Loaded Cart 45 units 31 units -14 units Total

Momentum and Impulse Questions What is the momentum of an object that is not moving? 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. 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? 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. 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 Answers 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. 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. 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. (80 N)(0.1s) = 8 Ns (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 Questions 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. 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. 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. 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 Answers 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 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 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 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 3 – the momentum is the same (but in the opposite direction )but the velocity for the bullet is much greater because its mass is less 2 – acceleration depends on mass

Sources Conceptual Physics by Paul Hewitt www.physicsclassroom.com http://rigel.physics.unr.edu/faculty/phaneuf/classinfo/index100.html