What is Momentum? Momentum is a commonly used term in sports. Momentum in Physics; it refers to the quantity of motion that an object has. Momentum can be defined as "mass in motion". The amount of momentum that 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. What is Momentum? Momentum may be defined by its equation: Momentum is a quantity defined as the product of the mass and velocity of an object. momentum = mass x velocity p = mv Unit of Momentum • The equation illustrates that momentum is directly proportional to an object’s mass and the object’s velocity. p = mv Large Momentum Examples Huge ship moving at a small velocity P = Mv High velocity bullet P = mv Momentum (p) = mass x velocity • A really slow moving truck and an extremely fast roller skate can have the same momentum. Momentum: Sample Problem Momentum: Sample Problem Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. p = 540 kg•m/s, east b. 1000-kg car moving northward at 20 m/s p = 20 000 kg•m/s, north c. 40-kg freshman moving southward at 2 m/s. p = 80 kg•m/s, south Momentum: Sample Problem A car possesses 20 000 units of momentum. What would be the car's new momentum if ... a. its velocity was doubled. p = 40 000 units (doubling the velocity will double the momentum) Momentum: Sample Problem A car possesses 20 000 units of momentum. What would be the car's new momentum if ... b. its velocity was tripled. p = 60 000 units (tripling the velocity will triple the momentum) Momentum: Sample Problem A car possesses 20 000 units of momentum. What would be the car's new momentum if ... c. its mass was doubled (by adding more passengers and a greater load) p = 40 000 units (doubling the mass will double the momentum) Momentum: Sample Problem A car possesses 20 000 units of momentum. What would be the car's new momentum if ... d. both its velocity was doubled and its mass was doubled. p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum; the combined result is that the momentum is doubled twice -quadrupled) Momentum Objects which aren’t moving have no velocity, and therefore have no momentum Momentum Examples A large truck has more momentum than a car moving at the same speed because it has a greater mass. Which is more difficult to slow down? The car or the large truck? MOMENTUM • Decreasing Momentum • Which would be safer to hit in a car ? mv mv Ft Ft • Knowing the physics helps us understand why hitting a soft object is better than hitting a hard one. MOMENTUM • In each case, the momentum is decreased by the same amount or impulse (force x time) • Hitting the haystack extends the impact time (the time in which the momentum is brought to zero). • The longer impact time reduces the force of impact and decreases the deceleration. • Whenever you need to decrease the force of impact, extend the time of impact! Changing Momentum • A change in momentum takes force and time. To stop an object, it is necessary to apply a force against its motion for a given period of time. Changing Momentum In football, the defensive player applies a force for a given amount of time to stop the momentum of the offensive player with the ball. Changing Momentum Changing Momentum • A force is applied to an object to change its momentum. • Impulse – the product of the force, and the time over which the force is applied. • Impulse – Momentum Theorem – the impulse experienced by the object equals the change in momentum Changing Momentum Force and Momentum Assume the force and acceleration are constant Since momentum is mass times velocity, the force can be related to the momentum This is the impulse theorem Section 7.2 Impulse Newton’s Second Law can read SF = ma = m(Dv/Dt) = (Dmv)/(Dt) = (Dp/ Dt) Rearranging, Impulse = Dp = FDt Sample Problem: Force needed for change in momentum (impulse) 0.3 s Sample Problem: Force acting on a car while braking. Impulse Impulse: The change in momentum of an object due to a force that is applied during a period of time Variable: J impulse = force x time J = Ft Units: N.s Use the impulse-momentum change principle to fill in the blanks in the following rows of the table. As you do, keep these three major truths in mind: • The impulse experienced by an object is the force•time. • The momentum change of an object is the mass•velocity change. • The impulse equals the momentum change.
