Momentum

1. Topic – Physics 2a Momentum

2. What is momentum? • Think about a foam ball and a cricket ball hitting a window. • Both are about the same size so why would only one break the window?

3. What is momentum? • Momentum is the mass of an object times the velocity of that object •  = mv • p= momentum in kgms-1 ; m = mass in kg ; v = velocity in ms-1

4. Link to equation • The cricket ball can have a mass of about 160 g while the foam ball has a mass of about 20 g. If both are thrown at 15 ms-1 you can quickly see that there is a large different in momentum and the cricket ball has a much larger effect on the window. cricket ball = mv foam ball = mv = 0.160 x 15 = 0.020 x 15 = 2.4 kgms-1 = 0.3kgms-1

5. Change in Momentum • You are leisurely riding home on your bike when it starts to rain. Quickly you increase your velocity to limit the time you get wet. Here you have experienced a change in momentum. The change in anything is the final minus the initial, • so • change in momentum = final momentum - initial momentum or •  = mv - mu

6. Example • Example: • While running in the park you are initially travelling at 3.50 ms-1 east. A dog runs out and starts to chase you so you increase your velocity to 6.00 ms-1 east. Assuming that your mass is 60.0 kg, what was your change in momentum? • m = 60.0 kg  = mv - mu • u = 3.50 ms-1 = m (v – u) = 60.0 (6.00 – 3.50) • v = 6.00 ms-1 = 60.0 x 2.5 •  = 1.50 x 102 kgms-1 east

7. A change in momentum can mean a change in direction • Example: • The 20.0 g foam ball hits the window at 15.0 ms-1 north and rebounds at 15.0 ms-1 south. What is the change in momentum? • m = 0.020 kg • u = 15.0 ms-1 north • v = 15.0 ms-1 south • V = (v – u)  = m (v – u) = m V • = (15.0 ms-1 south – 15 ms-1 north = 0.02 x 30 • = (15.0 ms-1 south + 15 ms-1 south)  = 0.600 kgms-1 south • = 30 ms-1 south Remember you cannot subtract a vector – it must be added with the direction reversed!

8. Impulse • If you are unlucky enough to have a car accident, you will experience a force on you that could cause injury or death. Car designers try to make cars as safe as possible, so to do this they try to decrease the force acting on you. In a car crash your velocity changes so you undergo a change in momentum, this can be re-written as • Ft = mv - mu F∆t=m∆v • Ft is known as impulse (units Ns (Newton seconds) and is equal to the change in momentum: • Impulse = Ft

9. Increase impact time • While the impulse (also known as impulsive force) can’t be changed, the time of the crash can. • Ifthe time over which the crash takes place is increased, the force must be decreased (simple maths). • To increase the time of the crash, car designers now design cars that crumple – this increases the time for the car to stop in a crash, thus decreases the force and possibly saving you from injury or death

10. Brick wall or hay stack This can be re-written as: Ft = mv - mu F∆t=m∆v Ft is known as impulse (units Ns) and is equal to the change in momentum: Impulse = Ft

11. Question???? How does hitting the haystack instead of the wall reduce the force acting on you?

12. answer • By hitting the haystack you extend the time of impact – you extend the time during which your momentum is brought to zero. Your change in momentum will be the same (impulsive force is the same), but the longer the time over which the change in momentum occurs, the less the force on you. If you extend the time of impact 100 times, you reduce the force of impact by 100. • Now complete activity 1,2,3

13. Answers to activity 1)People often put ‘roo bars’ on the front of their cars. What is the purpose of this? • To protect the front of the car from animals. • How does this affect the safety aspect of the car in a crash? • Unless roo bar crushes if you hit another car, then the roo bar prevents the front of the car from crumpling. Therefore the change of momentum happens over a very short time so the force on the people in the car will be much greater than if the front crumpled. Ft =  = m(v – u). 2)Why do you move your hand away from a high-speed ball upon contact instead of towards the ball? •  = m(v – u) = Ft. The change of momentum is a constant (can’t change mass, initial and final velocity). By moving your hand backwards, the time of impact is increased so the force on your hand is decreased. 3)Why do they have sand under playground slides instead of concrete? • As above, the sand increases the time over which the change of momentum occurs and as a result decreases the force on the child when they hit the sand.

15. Answers to activity

16. Formulas to remember • Force = mass x acceleration (F = ma) • Force = mass (v-u) ∆t • F∆t=m∆v (IMPULSE) • Momentum = Mass x change in velocity •  = mv •  = mv - mu •  = m (v – u) = m V