MOMENTUM: Inertia in motion Linear momentum of an object equals the product of its mass and velocity Moving objects have momentum Vector quantity The momentum vector points in the same direction as the velocity vector Proportional to mass and velocity p = mv p = momentum (kg * m/s) m = mass (kg) v = velocity (m/s)
Collisions: Momentum- Useful concept when applied to collisions In a collision, two or more objects exert forces on each other for a brief instant of time, and these forces are significantly greater than any other forces they may experience during the collision
What is the taxi cab’s momentum? * Mass of the taxi = 0.14 kg * Velocity of the taxi = 1.2 m/s Answer:p = mv p = (0.14 kg)(1.2 m/s) p = 0.17 kg * m/s to the left v = 1.2 m/s p = 0.17 kg * m/s
ΣF = Δp/Δt **Net force equals the change in momentum per unit time Rearranging this equation Δp = ΣFΔt Impulse (J) The change in momentum is called the impulse of the force (Impulse- momentum theorem) Vector quantity Units: kg * m/s J = Δp = FΔt p = Momentum J = Impulse F = Force Δt = Elapsed time The greater the net force, or the longer the interval of time it is applied, the more the object’s momentum changes the same as saying the impulse increases
Changing Momentum: Scenario 1 if you want to decrease a large momentum, you can have the force applied for a longer time. If the change in momentum occurs over a long time, the force of impact is small. Examples: Air bags in cars. Crash test video FtFt
Changing Momentum: Scenario 2 If the change in momentum occurs over a short time, the force of impact is large. FtFt
Baseball player swings a bat and hits the ball, the duration of the collision can be as short as 1/1000 th of a second and the force averages in the thousands of newtons The brief but large force the bat exerts on the ball = Impulsive force
A long jumper's speed just before landing is 7.8 m/s. What is the impulse of her landing? (mass = 68 kg) J = p f – p i J = mv f – mv i J = 0 – (68kg)(97.8m/s) J = -530 kg * m/s *Negative sign indicates that the direction of the impulse is opposite to her direction of motion
Impulse = Change in momentum J = Δp = F avg Δt Change in momentum Δp = mΔv ** In conclusion, there are different equations for impulse J = F Δt J = Δp = mΔv = mv f – mv i F Δt = mΔv
Conservation of momentum: The total momentum of an isolated system is constant No net external force acting on the system Momentum before = Momentum after
Momentum p = mv Conservation of momentum Momentum before = Momentum after p i1 + p i2 +…+ p in = p f1 + p f2 +…+ p fn m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2 m 1, m 2 = masses of objects v i1, v i2 = initial velocities v f1, v f2 = final velocities
Elastic collision Objects start apart and end apart Inelastic collision Objects start apart and end together Objects start together and end apart Momentum is conserved in any collision Elastic or inelastic
A 55.0 kg astronaut is stationary in the spaceship’s reference frame. She wants to move at m/s to the left. She is holding a 4.00 kg bag of dehydrated astronaut chow. At what velocity must she throw the bag to achieve her desired velocity? (Assume the positive direction is to the right.)
VARIABLES: Mass of astronaut m a = 55 kg Mass of bag m b = 4 kg Initial velocity of astronaut v ia = 0 m/s Initial velocity of bag v ib =0 m/s Final velocity of astronautv fa = -0.5 m/s Final velocity of bag v fb = ? EQUATION: m 1 v i1 + m 2 v i2 = m 1 v f1 + m 2 v f2 m a v ia + m b v ib = m a v fa + m b v fb 0 = m a v fa + m b v fb V fb = - (m a v fa / m b ) V fb = - ((55kg)(-0.5m/s))/(4kg) = m/s
Momentum is always conserved in a collision Classification of collisions: ELASTIC Both energy & momentum are conserved INELASTIC Momentum conserved, not energy Perfectly inelastic -> objects stick Lost energy goes to heat
Catching a baseball Football tackle Cars colliding and sticking Bat eating an insect Examples of Perfectly Elastic Collisions Superball bouncing Electron scattering Examples of Perfectly Inelastic Collisions