An automobile has a mass of 2300 kg and a velocity of 16 m/s. It makes a rear-en

Question

An automobile has a mass of 2300 kg and a velocity of 16 m/s. It makes a rear-end collision with a stationary car whose mass is 1800kg. The cars lock bumpers and skid off together with the wheels locked.
(a) What is the velocity of the two cars just after collision?
(b) Find the impulse (magnitude and direction) that acts on the skidding cars from just after the collision until they come to rest.
(c) If the coefficient of kinetic friction between the wheels of the cars and the pavement is k = 0.80, determine how far the cars skid before coming to rest.

Explanation / Answer

a) This collision is completely inelastic. Therefore, it can be assumed that the initial momentum = final momentum. (m1)velocity(initial)=(m2+m1)(velocity(final)). If you solve for the final velocity, you will get the final velocity. b)The impulse is the integral of mass times acceleration, or also the change in momentum. So, the change of momentum of the first car will be the impulse. c) Using that the cars are stuck together, you can find their normal force ( m1+m2) times (9.8). Then, to find the force of friction countering motion, you must use that (µk(normal force)= decelerator force). This force can yield your acceleration, which you then plug into the formula (change in position = (original velocity times time)+ (1/2 of acceleration times time squared.))

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