Nathan R.
asked • 10/14/20A blue car with mass mc = 459 kg is moving east with a speed of vc = 19 m/s and collides with a purple truck with mass mt = 1246 kg that is moving south with a speed of vt = 10 m/s . The two collide and lock together after the collision.
1) What is the magnitude of the initial momentum of the car?
2) What is the magnitude of the initial momentum of the truck?
3) What is the angle that the car-truck combination travel after the collision? (give your answer as an angle South of East)
4) What is the magnitude of the momentum of the car-truck combination immediately after the collision?
5) What is the speed of the car-truck combination immediately after the collision?
NOTE: ANSWER all questions since they correspond with each other and make sure to label or bold each answer and be able to respond back if its wrong
Jeffrey K. answered • 10/19/20
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Hello, Nathan.
This question requires the principle of Conservation of Momentum, meaning that total momentum = mv is the same before and after a collision.
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Jeffrey K.
Sorry, the system, in its great wisdom, closed my answer out before it was complete! Here's the rest of the answer: Questions 1 and 2 simply require calculation of momentum = mv I leave this as an exercise for you. For Q3, we consider the total momentum in the north/south and east/west directions, separately. We can do this because they are orthogonal (at right angles), so can't affect each other. Total momentum, east/west, before collision = mc x vc + 0 = 459 x 19 = 8,721 kg m/s Total momentum, east/west, after collision = (459 + 1,246) vf cos A where vf = final velocity of the joined masses and A = angle made with the east/west axis. By conservation of momentum: 1,705 vf cos A = 8,721 . . . . . . . . (1) Similarly, north/south momentum before = 0 - 1,246 x 10 = -12.460 (minus => south) And north/south momentum after = (459 + 1,246) vf sin A By conservation of momentum: 1,705 vf sin A = -12,460 . . . . . . . . (2) Now, we can solve (1) and (2). Let's eliminate vf by dividing (1) by (2). This gives sin A / cos A = -12,460 / 8,721 or tan A = -1.43 A = -55 degrees (south of east) Substitute this into (1) or (2) and find vf. Q4. The required momentum, after collision, is the sq root of the sum of the north/south momentum squared plus the east/west momentum square. Both of these momenta are calculated above. Q5. The required final velocity, after collision, vf, is calculated above.10/19/20