Answer to Question #200297 in Mechanics | Relativity for Gil Dror

Question

Two carts 1 and 2 move along a straight line towards each other as shown in Figure A and collide head-on. The graph shown in the diagram depicts the force F12 exerted by cart 1 on cart 2 during the collision, as a function of time, direction and positive is selected to be in the right direction. Given that the mass of cart 1 is m1 = 0.2kg and its velocity before the collision is v1 = 3m / s in the positive direction, and the mass of the cart 2 m2 = 0.8kg and its velocity before the collision is v2 = 3m / s in the negative direction.

A. Copy the graph in Figure B to your page and add to this graph (in the same system of axes) a graph depicting the force exerted by cart 2 on cart 1 (force F21) during the collision. 

B Calculate the speed of each of the carts immediately after the collision. 

C. Is the collision completely elastic? Necrosis. 

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Answer 1

Part a

Part b

Consider the conservation of momentum

$(m_1v_1+m_2v_2)_i=(m_1v_1+m_2v_2)_f$

$0.2*3+0.8*3=0.2v_1+0.8v_2$

$0.2v_1+0.8v_2=3$

Also, consider conservation of kinetic energy

$(v_1)_i+(v_1)_f=(v_2)_i+(v_2)_f$

$3+v_1=3+v_2$

$v_1=v_2$

$0.2v_1+0.8v_1=3$

$v_1=3m/s \implies v_2 =3m/s$

Part 3

This is a completely elastic collision. There is no loss of kinetic energy in the collision.