A 480 kg car moving at 14.4 m/s hits from behind another car moving at 13.3 m/s

Question

A 480 kg car moving at 14.4 m/s hits from behind another car moving at 13.3 m/s in the same direction. If the second car has a mass of 570 kg and a new speed of 17.9 m/s, what is the velocity of the first car after the collision? A girl of mass 55 kg throws a ball of mass 0.8 kg against a wall. The ball strikes the wall horizontally with a speed of 25 m/s, and it bounces back with this same speed. The ball is in contact with the wall 0.05 s. What is the average force exerted on the wall by the ball? 4.00 Times 10^5 J of work are done on a 1110 kg car while it accelerates from 10.0 m/s to some final velocity. Find this final velocity. A heat engine has a maximum possible efficiency of 0.800. If it operates between a deep lake with a constant temperature of 287.0 K and a hot reservoir, what is the temperature of the hot reservoir? How many moles of an ideal gas are there in a container with a pressure of 108.893 Pa, a temperature of 321 K, and a volume of 2.0 L? The universal gas constant is 8.314 J/K mol.

Explanation / Answer

1) Before the collision the momentum of the first car is 480*14.4=6912

The momentum of the second car is 570*13.3=7581

6912+7581=14493=total momentum of system

After the collision the second car has a momentum of 570*17.9=10203

Subtract this from the total momentum to get the momentum of the first car 14493-10203=4290

Divide 4290 by the cars mass to get the cars velocity 4290/480=8.9375 m/s

2) The acceleration = (v/t) = 25/(0.05/2) = 1,000m/sec^2.
Force = (ma) = 0.8 x 1,000, = 800N. average.

3) By doing a wok on the car, it gets accelerated to certain velocity attaining certain amount of kinetic energy. At the end of this work, the measure of the energy attained is a measure of the work done. Hence,
½ m v² = Work done
½ m v² = 4 x 10^5 Joules
½ x 1110 x v² = 400000
v² = 400000 / (½ x 1110) = 400000 / 555 = 720.72
v = 720.72 = 26.846 m/s

4) 1440 K

5) use the ideal gas law : PV = nRT

here, P = 108893 Pa

V = 2 L = 2 * 10^(-3) m^3

R = 8.314 J / K mol

T = 321 K

then n= 0.08 mole

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