Momentum Momentum is a commonly used term in sports. –A–A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop.

More force is needed to quickly stop a baseball thrown at 95 mph than to quickly stop a baseball thrown at 45 mph, even though they both have the same mass. More force is needed to quickly stop a train moving at 45 mph than to quickly stop A car moving at 45 mph, even though they both have the same speed. Both mass and velocity are important factors when considering the force needed to change the motion of an object.

the product of mass and velocity of an object momemtum = mass x velocity p = mv p = momentum Units: kg m/s

Example: If a 100 kg person is running with a velocity of 5m/s, how much momentum does the person have?

Momentum is a vector, so direction is important. An object’s momentum will change massvelocity if its mass and/or velocity (speed or direction) changes. According to Newton’s laws, a net force causes an object to accelerate, or change its velocity. A net force, therefore, causes a change in an object’s momentum.

F Net = ma (Newton’s Second Law) Impulse = change in momentum

Impulse A force acting for a given amount of time will change an object's momentum. –Put another way, an unbalanced force always accelerates an object – either speeding it up or slowing it down. If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed.

Impulse (J) In both cases the impulse will be the same By moving with the punch it decreases the ‘sting’

A 1000 kg car moving at 30 m/s (p = 30,000 kg m/s) can be stopped by 30,000 N of force acting for 1.0 s (a crash!) or by 3000 N of force acting for 10.0 s (normal stop)

Example

Formulas P = momentum (kg m/s) m = mass (kg) v = velocity (m/s) J = impulse (N s) F = force (N) t = time (s) Δ = change (final – initial)

The momentum of any closed, isolated system does not change. The momentum before an event, p 1, is equal to the momentum after the event, p 2. p 1 = p 2 m 1 v 1 + m 2 v 2 + m 3 v 3 + … = m 1 V 1 + m 2 V 2 + m 3 V 3 + … where v is the velocity before the event and V is the velocity after Reference Table

Collisions Elastic Objects strike each other and bounce off. Inelastic Objects strike each other and stick together. Explosions Objects start out together and then break apart

Elastic

Inelastic

Graphical Representation Momentum and Impulse can be represented in graphs. –Velocity vs. Time –Force vs. Time F t V t

Velocity vs. Time When the graph has velocity vs. time remember: –mΔv = Δp = J –F*t = Δp = J What is the change in momentum for section (A)? What force is required to impart that change in momentum? What is the acceleration? m = 5 kg

Force vs. Time m = 5 kg When the graph has force vs. time remember: –The area under the curve represents the impulse –F*t = Δp = J –F = m*a What is the change in momentum for section (B)? What is the acceleration? What is the final velocity at the end of that section