Question

Two cars collide at right angles and stick together as they skid to a stop. Car 1 has a mass of 1300 kg and a speed of 21 km/h to the east. Car 2 has a mass of 1000 kg and a speed of 36 km/h to the north. The average coefficient of friction between the tires and the road is 0.65. How far from the collision point, and in what direction, do the cars stop?

Answer 1

Answer:

The cars stop 2.34 m from the collision point and move in the direction dictated by the velocity, 52.8°.

Explanation:

Mass of first car = 1300 kg

Velocity of first car = (21î) km/h = (5.833î) m/s

Mass of second car = 1000 kg

Velocity of second car = (36j) km/h = (10j) m/s

Let the velocity of both cars after collision be v

Using the law of conservation of Momentum.

Momentum before collision = momentum after collision

Momentum of first car before collision = (1300)(5.833î) = (7582.9î) kgm/s

Momentum of second car before collision = (1000)(10j) = (10000j) kgm/s

Momentum of both cars after collision = (1300+1000)v = 2300v

Momentum before collision = momentum after collision

(7582.9î) + (10000j) = 2300v

v = (3.30î + 4.35j) m/s

Magnitude of v = √(3.30² + 4.35²) = 5.46 m/s

Direction of v = tan⁻¹ (4.35/3.30)

Direction of v = 52.8°

Then using the work-energy theorem,

The kinetic energy of the two joint cars = Work done by frictional forces in stopping the joint cars.

Kinetic energy of the cars after collision = (1/2)(2300)(5.46²) = 34,283.34 J

Work done by frictional force = F × d

where F = frictional force = μmg = (0.65)(2300)(9.8) = 14,651 N

d = distance over which the frictional force acts before stopping the two cars = ?

34,283.34 = 14,651d

d = (34,283.34/14,651)

d = 2.34 m

Therefore, the cars stop 2.34 m from the collision point and move in the direction dictated by the velocity, 52.8°.

Hope this Helps!!!