A speeding truck, with a mass of 1200 kg, slams into the back of a stationary ca

Question

A speeding truck, with a mass of 1200 kg, slams into the back of a stationary car, with a mass of 1000 kg, at a stop light. The two vehicles slide together, eventually coming to rest 40 m from the point of impact. In addition to measuring the length of the skid mark after the collision, the investigating officer measured the static and kinetic coefficients of friction between the wreckage and the road to be 0.45 and 0.35, respectively.

a. What is velocity of the truck and car immediately after the collision?

b. What is the velocity of the truck just before striking the car?

c. How much thermal energy is generated in this collision?

Please give a thorough explanation for all work. Physics is a difficult subject for me and for me to succeed in this class I really need to understand how you arrived at each answer – thanks!

Explanation / Answer

A)let before collision truck velocity be a

and after collision combined velocity of truck and car is b then

from momentum conservation

1200a=3200b

also deceleration= friction on truck+friction on car/3200

=0.45x9.81x1200+0.35x9.81x1000/3200=2.73m/s2

now from 3rd equation of motion

02=b2-2x2.73x40

b=14.78m/s

velocity before hitting a=3200x14.78/1200=39.41m/s

thermal energy=1/2x1200x39.412-1/2x3200x14.782 = 582371.42 J (loss of kinetic energy=themal energy)

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