A 9230-kg truck collides head on with a 1250-kg parked car. The vehicles entangle together and slide a linear distance of 10.6 meters before coming to rest. Assuming a uniform coefficient of friction of 0.820 between the road surface and the vehicles, determine the pre-collision speed of the truck.

Question

Mathematics

Madalynn

2 August, 07:52

A 9230-kg truck collides head on with a 1250-kg parked car. The vehicles entangle together and slide a linear distance of 10.6 meters before coming to rest. Assuming a uniform coefficient of friction of 0.820 between the road surface and the vehicles, determine the pre-collision speed of the truck.

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Cassandra Stanley · Answer 1

=>By the work energy relation:-

=>W = ∆KE

=>Ff. s = 1/2 (M+m) v^2

=>µk x N x s = 1/2 (M+m) v^2

=>µk x (M+m) x g x s = 1/2 (M+m) v^2

=>v = √[2µkgs]

=>v = √[2 x 0.82 x 9.8 x 10.6]

=>v = 13.05 m/s

By the law of momentum conservation:-

=>Mu = (M+m) v

=>9230u = (9230+1250) x 13.05

=>u = 14.82 m/s