A 1050 kg sports car is moving westbound at 13.0 m/s on a level road when it col

Question

A 1050 kg sports car is moving westbound at 13.0 m/s on a level road when it collides with a 6320 kg truck driving east on the same road at 11.0 m/s . The two vehicles remain locked together after the collision.

Part A

What is the velocity (magnitude) of the two vehicles just after the collision?

Part B

What is the direction of the velocity of the two vehicles just after the collision?

to the east

Part C

At what speed should the truck have been moving so that it and car are both stopped in the collision?

Part D

Find the change in kinetic energy of the system of two vehicles for the situations of part A.

Part E

Find the change in kinetic energy of the system of two vehicles for the situations of part C.

to the east

Part C

At what speed should the truck have been moving so that it and car are both stopped in the collision?

Part D

Find the change in kinetic energy of the system of two vehicles for the situations of part A.

Part E

Find the change in kinetic energy of the system of two vehicles for the situations of part C.

Explanation / Answer

A) Magnitude of the velocity just after collision 7.5 m/s

Momentum is conserved in the collision

Total momentum after collision = 6320 x 11 - 1050 x 13 = 55870 kg-m/s East ward

Total mass = 6320 + 1050 = 7320 kg

Velocity after collision = 55879/7320 = 7.5 m/s

B) Velocity of the two vehicles after collision is 7.5 m/s towards east.

C) Let v be the speed of the truck so that the two vehicles stop after collision, the the momentum in east and west direction shall be equal so that net momentum is 0 after collision

6320 x v = 1050 x13

Speed of the truck v = 1050 x13 /6320 = 2.16 m/s

D) KE before collision = (1050*13^2 + 6320 x 11^2)/2 = 471085 J

    KE after collision = 7320 x (7.5)^2 /2 = 207281 J

    Loss of KE = 471085 - 207281 = 263804 J

E) with situation in Part C

KE before collison = (1050 * 13^2 + 6320 * 2.5^2)/2 = 108475 J

Since both vehicles have stopped after collision, entire KE is lost.

Change in KE =108475 J

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