Physics Momentum: Collisions

Transcription

1 F A C U L T Y O F E D U C A T I O N Departent o Curriculu and Pedagogy Physics Moentu: Collisions Science and Matheatics Education Research Group Supported by UBC Teaching and Learning Enhanceent Fund 1-13

2 Two Block Collisions

3 Question Title Colliding Blocks I Block A has an initial elocity. Block B is stationary and has twice the ass o block A. Block A Block B Block A collides into Block B. Consider the syste consisting o only blocks A and B. Which o the ollowing orces are internal? A. The orce Block A exerts onto Block B and ise-ersa, due to the collision: F AonB and F BonA B. The graitational orce the earth exerts onto the blocks, F gona and F gonb C. The noral orce the table exerts onto the blocks, F NonA and F NonB D. The riction orce exerted by the table onto the blocks, F ricona and F riconb E. All o the aboe

4 Solution Answer: A Justiication: The orces internal to the syste are the orces exerted by the objected included in the syste. In our case these are the orces blocks exert onto each other since the syste consists only o Block A and Block B. The orces exerted by objects in the surroundings (such as the earth and table) onto the syste are the external orces.

5 Question Colliding Blocks Title II Block A Block B During the collision, Block A exerts a orce F AonB onto Block B, while Block B exerts a orce F BonA onto Block A. Which o the ollowing correctly describes the relationship between F AonB and F BonA? A. F BonA =.5 F AonB B. F BonA = F AonB C. F BonA = F AonB D. F BonA = 4 F AonB

6 Solution Answer: B Justiication: According to Newton s Third Law: F F B on B on A A F A on B Thereore, internal orces cannot generate a net orce on a syste and thus cannot change the oentu o the syste (the two blocks). Assuing no riction and F g = -F N, there will be no external net orce on the syste. F A on B F net p t sys

7 Question Colliding Blocks Title III Initial State: Block A Block B According to the law o oentu conseration, which o the ollowing is NOT a possible inal state ater the collision? Assue no riction. A. 3 3 B. C. D. 3

8 Solution Answer: B Justiication: Moentu is consered in all the collisions except or B. p i ( ) p Since the inal oentu o the syste does not equal the initial oentu, this collision outcoe is not possible. Additionally, the inal kinetic energy in B is greater than the initial kinetic energy o the syste. The echanical energy o the syste cannot increase as a result o collision, it can only decrease.

9 Question Colliding Blocks Title IV Initial State: Block A Block B Jerey ust predict the inal state o the collision. Ater taking conseration o oentu into consideration, Jerey coes up with the ollowing inal state: Is this collision outcoe possible? A. Yes B. No C. Cannot be deterined

10 Solution Answer: B Justiication: Moentu is consered in the proposed collision. Howeer, the inal kinetic energy is 3 ties larger than the initial kinetic energy. E E k, i k, () 3 The inal kinetic energy ay be less than or equal to the initial kinetic energy, but not greater.

11 Question Colliding Blocks Title V Initial state: Block A Block B Final states: Rank the inal states ro greatest to least kinetic energy. (Moentu is consered in all these collisions) A. E k, 1 > E k, 3 > E k, > E k, 4 C. E k, 1 > E k, > E k, 3 > E k, 4 B. E k, 3 > E k, 1 > E k, > E k, 4 D. E k, 1 > E k, 3 > E k, 4 > E k,

12 Solution Answer: A E k,1 > E k,3 > E k, > E k,4 Justiication: Kinetic energy is a scalar quantity that depends on speed, unlike oentu which depends on elocity. Collision 1 has the ost kinetic energy since Block A is oing let. In order to consere oentu, Block B ust hae a large elocity towards the right. In collision 3, Block A is no longer oing let but is now stationary. Block B ust hae a saller elocity to the right than in collision 1 in order to consere oentu because o its larger ass. In collision, both blocks are oing to the right. Thus both blocks ust be oing slowly in order to hae a inal oentu equal to. Collision 4 has the least kinetic energy since it is the axially inelastic case where the two blocks stick together ater the collision.

13 Question Colliding Blocks Title VI Final state: Block A Block B Suppose that ater Block A and Block B collide, both blocks are at rest. All the kinetic energy has been transerred into other ors o energy such as heat. Which o the ollowing ust hae been the initial state o the collision? A. B. A A B C. A B D. B E. All o the aboe initial states are possible

14 Solution Answer: C Justiication: In the inal state with both Block A and B at rest, there is no oentu and no kinetic energy. The initial oentu o the two blocks beore the collision ust hae been zero. Collisions A, B, and D are not possible because they hae an initial oentu. In collision B, Block A and Block B are oing in opposite directions. I Block A is oing twice as ast as Block B, then it is possible or the initial oentu to be zero.

15 Question Title Colliding Block VII (Hard) A block with initial elocity is sliding towards a larger stationary block with unknown ass. Ater they collide elastically, the two blocks are oing at the sae speed but in opposite directions. Final state M M Initial state Based on this inoration, what ust be true about the relatie asses o M and? A. M = D. M = 4 B. M = E. M = ½ C. M = 3

16 Solution (Part 1) Answer: C Justiication: Deine x such that M = x. Fro the law o conseration o oentu: x x ( x 1) Fro conseration o energy (collision is elastic): x x ( x 1) Equation 1 Equation

17 Solution (Part ) Substituting equation 1 into gies: ( x 1) ( x 1) x 3x ( x 1) ( x 1) x 3 or x since Thereore, ass M ust be 3 ties as large as ass. 3 Substituting x = 3 back into equation 1 shows that both the sall ass and the larger ass will be oing at hal the initial elocity.