Higher Physics Unit Momentum and Impulse

Transcription

1 Higher Physics Unit.4 Momentum and Impulse

2 Momentum The momentum of an object is the product of it s mass and velocity. The MOMENTUM of an object is calculated by: p = m v velocity (ms - ) momentum (kg ms - ) mass (kg) Momentum is a vector (has both magnitude and direction).

3 Collisions Before Collision After Collision ms - stationary ms - stationary

4 Before Collision After Collision ms - stationary ms - stationary

5 Results Before Collision After Collision Mass Velocity Mass Velocity Conclusion BEFORE AFTER mass velocity = mass velocity MOMENTUM IS CONSERVED

6 Momentum and Collisions The total momentum is CONSERVED in collisions provided there are no external forces (e.g. friction). v v v 3 m m => m m total momentum before = total momentum after m + ( m m ) 3 v + m v = v

7 Example A 7kg mass travelling at 8 ms - collides and sticks to a stationary 4 kg mass. Calculate the velocity just after impact. 8 ms - v 7kg 4kg 7kg 4kg stationary total momentum before = total momentum after m v + m v = ( m + m ) v 3 ( 7 8) + ( 4 0) = v v = v = ms - to the right

8 Example A car of mass,000 kg is travelling at 5 ms -. It collides and joins with a,00 kg car travelling at 3 ms -. Calculate the velocity of the cars just after impact. 5 ms - 3 ms - v kg 00 kg 000 kg 00 kg total momentum before = total momentum after m v + m v = ( m + m ) v 3 ( 000 5) + ( 00 3) = 00 v 00 v = v = ms - to the right

9 Worksheet Momentum and Collisions Q Q6

10 Is Momentum Conserved? Diagram Electronic Timer Light Gate m m linear air track

11 Procedure Vehicle is sprung along the air track. It breaks the first light gate and a velocity is given. It collides and sticks to the second vehicle. They both move together and break the second light gate, giving a second velocity. Results m = kg m = kg m 3 = kg - v = ms - v = ms - v 3 = ms

12 total momentum before = m + v m v = + = - kg ms total momentum after = = = m 3 v kg ms Conclusion Momentum is CONSERVED. total momentum before = total momentum after

13 Elastic Collisions KINETIC ENERGY CONSERVED MOMENTUM CONSERVED Example A 00 kg vehicle is travelling at 6 ms - when it collides with a stationary 00 kg vehicle. After the collision, the 00 kg vehicle moves off at ms - and the 00 kg vehicle at 8 ms -. Show the collision is elastic.

14 6 ms - ms - 8 ms - 00 kg 00 kg 00 kg 00 kg stationary Momentum Before After m + v m v - 00 kg ms m + v3 m v4 ( 00 6) + ( 00 0) ( 00 ) + ( 00 8) - 00 kg ms Momentum has been conserved.

15 Kinetic Energy Before After K v m E = + = E K = 3600 J K v m E = + = E K = 3600 J Kinetic Energy has been conserved. As momentum and kinetic energy are conserved, ELASTIC collision.

16 Inelastic Collisions Kinetic Energy NOT Conserved MOMENTUM CONSERVED Example A trolley of mass 3 kg is travelling at 5 ms - when it collides with a stationary kg trolley. Afterwards, they move off at 3 ms - and 6 ms - respectively. Show that this collision is inelastic.

17 5 ms - 3 ms - 6 ms - 3 kg kg 3 kg kg stationary Momentum Before After m + v m v - 5 kg ms m + v3 m v4 ( 3 5) + ( 0) ( 3 3) + ( 6) - 5 kg ms Momentum has been conserved.

18 Kinetic Energy Before After K v m E = + = E K = 37.5 J K v m E = + = E K = 3.5 J Kinetic Energy has NOT been conserved. As momentum is conserved and kinetic is not, INELASTIC collision.

19 TOTAL ENERGY is always CONSERVED total energy = kinetic energy + heat energy + sound energy Note In reality, most collisions are inelastic. Some of the kinetic energy is converted to heat and sound energy on impact.

20 Worksheet Elastic and Inelastic Collisions Q Q3

21 Head On Collisions Head on collisions involve objects travelling in opposite directions. One direction is POSITIVE, the other then has to be NEGATIVE. Example A 4 kg object travels at ms - and collides head on with a 3 kg object travelling with a speed of 7 ms -. After the collision, they both move off together. (a) (b) calculate the velocity of the objects just after impact. determine whether the collision is elastic or inelastic.

22 (a) ms - -7 ms - v 4 kg 3 kg 4 kg 3 kg total momentum before = total momentum after m v + m v = ( m + m ) v ( 4 ) + ( 3 (-7 )) = ( 4 + 3)v 7 v = 7 v = v = ms to the right

23 (b) Kinetic Energy Before After E = K m v E = K m v = (-7) = = E K = 36.5 J E K = 5. J Kinetic Energy has NOT been conserved. INELASTIC collision.

24 Example Two objects collide as shown. 5 ms - -3 ms - ms - v 7 kg 4 kg 7 kg 4 kg (a) Calculate the velocity at which the 4 kg object moves, just after impact. (b) Determine whether the collision is elastic or inelastic.

25 (a) total momentum before = total momentum after m v + m v = m v + m 3 v4 ( 7 5) + ( 4 (-3)) = ( 7 ) + ( 4 v) 35 - = 4 + 4v 3-4 = 4v = 9 v = 4v -.5 ms to the right

26 (b) Kinetic Energy Before After E = K m v E = K m v = (-3) = = E K = 05.5 J = E K = 4.3 J Kinetic Energy has NOT been conserved. INELASTIC collision.

27 Explosions In all explosions: MOMENTUM CONSERVED BEFORE v AFTER v stationary m m

28 total momentum before = total momentum after m v = m + v m v (-v ) m 0 = m + v 0 = - m + v m v Example A 5 kg gun fires a 0. kg shell at 80 ms -. The gun recoils after firing the shell. Calculate the recoil speed of the gun.

29 BEFORE AFTER v 80 ms - 5 kg 0. kg 5 kg 0. kg stationary total momentum before = total momentum after m v = m + v m v ( v) + ( 0. 80) 0 = 5-5v = v = ms backwards

30 Example Two trolleys initially at rest and touching, fly apart when the plunger is released. One trolley with a mass of kg moves off with a speed of 4 ms -. The other trolley moves off in the opposite direction with a speed of 5 ms -. Calculate the mass of this trolley. -4 ms - 5 ms - kg m

31 total momentum before = total momentum after m v = m + v m v (-4) + ( m 5) 0 = 5m = 8 m =.6 kg

32 Worksheet Head On Collisions and Explosions Q Q8

33 Impulse & Change in Momentum Consider the following equations: F = m a a = v t u Combining these equations: F = m a F = m ( v -u) t F t = mv - mu

34 IMPULSE (F t) = CHANGE IN MOMENTUM (mv mu) force (N) F t = mv - mu initial velocity (ms - ) time (s) mass (kg) final velocity (ms - ) Impulse IMPULSE is the product of the FORCE and the TIME during which it acts. impulse = F t *** NOT ON DATA SHEET *** The units of impulse are N s (Newton Seconds). Impulse is a vector quantity.

35 Change In Momentum The change in momentum is the difference in momentum from when the object is moving at its initial speed until it reaches its final speed. change in momentum = mv - mu *** NOT ON DATA SHEET *** The unit of change in momentum is kg ms -.

36 Impulse and Change in Momentum Impulse and change in momentum are equal to each other. So if you know impulse is Ns, without any further calculation, you can state the change in momentum to be kg ms -. F t = mv - mu IMPULSE = CHANGE IN MOMENTUM

37 Example A golf ball of mass 50 g is hit off the tee at 30 ms -. The time of contact between club and ball is 5 ms (milliseconds). Calculate the average force exerted on the ball. m = 50 g = 0.05 kg - u = 0 ms - v = 30 ms t = 5 ms = s F F t = mv - mu 3 ( 5 0 ) = ( ) - ( ) F = F = N -3

38 Impulse, Force and Time impulse = area under force-time graph force / N force / N time / s time / s impulse = = area under graph b h impulse = = area under graph l b + b h

39 Example A 50 g golf ball is hit off the tee by a force which varies with time as shown. force / N 40 Calculate the speed of the golf ball off the tee time / ms impulse = area under graph = b h - ( 30 0 ) 40 3 = = 0.6 N s impulse = mv-mu 0.6 = 0.05 v v = v = v = ms

40 Change In Momentum Air Bags A passenger in a car involved in a collision will experience a force which will bring him to a stop. NO Air Bag Head hits hard object eg. steering wheel In contact for a short time Large force involved Lots of Damage AIR BAG Head hits air bag In contact for a longer time Smaller force involved Less damage

41 In both cases the change in momentum and therefore the impulse are the same. However, the force-time graphs will differ in shape although the area under the line will be the same. NO Air Bag Large force. Short time. force / N force / N AIR BAG Small force. Long time. time / s time / s area under each graph is the same Air bags decrease the rate of change in momentum.

42 Crumple Zone A car is designed with a crumple zone so that the front of the car collapses during impact. The purpose of the crumple-zone is to A B C D E decrease the driver s change in momentum per second increase the driver s change in momentum per second decrease the driver s final velocity increase the driver s total change in momentum decrease the driver s total change in momentum. Less damage is caused if the change in momentum is over a long period of time.

43 Top Gear - Lorry Challenge

44 Worksheet Impulse and Change In Momentum Q Q6

45 Rebounds Example A 5 kg tyre hits a wall at 4 ms - and rebounds at 3 ms -. 4 ms - 3 ms - Calculate the change in momentum of the tyre.

46 change in momentum = mv - mu = (-3) = 5 0 = 35 kg ms