Impulse & Momentum

What is momentum? Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. Momentum = mass x velocity In physics, the symbol for the quantity momentum is the small case "p"; thus, the above equation can be rewritten as

p = m x v

Momentum is a vector quantity. As discussed in an earlier unit, a vector quantity is a quantity which is fully described by both magnitude and direction. To fully describe the momentum of a moving object, you must include information about the direction of the object.

From the definition of momentum, it becomes obvious that an object has a large momentum if either its mass or its velocity is large. The momentum equation: (p = m x v) can help us to think about how a change in one of the two variables might effect the momentum of an object. The momentum is directly proportional to the mass and velocity. The mass is inversely proportional to the velocity.

Using the equation determine the momentum of: A) 60 kg halfback moving at 9 m/s. 540 kg-m/s B) 1000 kg car moving south at 20 m/s kg-m/s.

A car has units of momentum. What will happen to the momentum if: A) The velocity was doubled? units. B) The mass was tripled? units C) The mass and velocity were doubled? units

A force acting over time will change an object's momentum. If the force acts opposite the object's motion, it slows the object. If a force acts in the same direction as the object's motion, then the force speeds the object up.

Newton’s first law states an object in straight line motion will remain in motion unless acted on by an outside force. Since this force will change the object’s velocity, it will change the object’s momentum. The change in momentum caused by a force is called an impulse. Impulse is a vector quantity like momentum. The impulse acts in the same direction as the force. The strength of the impulse depends on two factors: The strength of the force and the time the force is applied.

Mathematically impulse = force x time. More importantly impulse is the change in momentum; therefore force x time = mass x change in velocity. Mathematically: F x t = m x  v Simply put, you apply a force to a moving object you will change its velocity.

Observe the above picture. What exerts the force providing an impulse to the car? From Newton’s Third Law, the tree exerts a force on the car equal to the force the car exerted on the tree.

The large force exerted by the tree brings the car to a quick stop. The result is the crushing of the car’s front end. The tree provided the impulse to stop the car by exerting a large force over a short time. Is there another option? Force and time are inversely proportional to each other. If you increase one the other decreases. If you increase the time of contact for a collision the force is reduced.

Force TimeImpulse Combinations of Force and Time Required to Produce 100 units of Impulse Notice what happens to the force as the time increases.

The boxer “rides” the punch, which increases the contact time of the punch which reduces the force of the punch.

Another example is the use of air bags in cars. When the air bag deploys they extend the time required to stop the momentum of the driver and passenger. When lacrosse players catch the ball the ball is "cradled" when caught; i.e., the lacrosse player reaches out for the ball and carries it inward toward his body as if he were cradling a baby. The effect of this strategy is to lengthen the time over which the collision occurs and so reduce the force on the lacrosse ball.

Which case has the greatest change in velocity? Case B 30 m/s – (-28 m/s) = = 58 m/s Case A 10 m/s – (-5 m/s) = = 15 m/s This type of collision is called a rebound.

A rebound is a collision involving a direction change in addition to a speed change. The result of the direction change is a large velocity change. In a rebound collision, an object will have the same or nearly the same speed as it had before the collision. Collisions in which objects rebound with the same speed (and thus, the same momentum and kinetic energy) as they had prior to the collision are known as elastic collisions. Elastic collisions are characterized by a large velocity change, a large momentum change, a large impulse, and a large force.

F x t = m x  v is the equation which connects the impulse to the change in velocity Force (N) Time (s) Imp ppm(kg) vv

Conservation of Momentum

What is the effect of a collision on objects? According to Newton’s Third Law colliding objects exert equal forces on each other. Unless the masses of the objects are equal, the colliding objects will have different accelerations. Equal forces mean equal impulses; therefore equal changes in momentum, and then the total momentum of the system will remain constant.

The rightward moving seven-ball experiences a leftward force which causes it to slow down; the eight-ball experiences a rightward force which causes it to speed up. Since the two balls have equal masses, they will also experience equal accelerations. In a collision, there is a force on both objects which causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction.

m 1 m 2 m 1  v = - m 2  v The above equation is one statement of the law of momentum conservation. In a collision, the momentum change of object 1 is equal and opposite to the momentum change of object 2. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

Money Conservation BeforeAfterChange Jack$100$50-$50 Jill$100$150+$50 Total$200$2000

Chris Angel Chris Angel The following link connects to a video of illusionist Chris Angel performing a stunt in which he survives being hit by a car while he is standing against a brick wall.

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..80 N-s Impulse = Force x time 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?.1 N-s Impulse equals the change in momentum. If you calculate the impulse you are calculating the change in momentum.

A 120 kg lineman moving west at 2 m/s tackles an 80 kg football fullback moving east at 8 m/s. After the collision, both players move east at 2 m/s. In which case is the momentum greater? A) Before the collision B) After the collision C) Neither case, the momentum is the same before and after the collision. Neither case, the momentum is the same before and after the collision.

80v + 40v = v = 480 v = 4 m/s What is the velocity of the grandmother after she grabs and holds on to him while rollerskating?

3000v = v = v = 5.0 m/s What is the velocity of the truck after colliding with the stationary car?