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Pi] A car's engine produces a useful output power of 6.5 10° W

The car of mass 950 kg is moving up a hill at a steady speed.
The slope of the hill is 12° to the horizontal. Resistive forces on the car are negligible.
1?
What is the steady speed of the car? rk
[1 mark]
A 7.0ms7 [e]
B 12ms7 [e]
Cc 34ms7 [=]
D 68ms7 [e]

Pi] A car's engine produces a useful output power of 6.5 10° W The car of mass 950 kg-example-1
User Daniel Miladinov
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1 Answer

10 votes
10 votes

Recall that

P = F v

where

P = power produced by the engine

F = magnitude of the component force supplied by the engine in the direction of the car's motion

v = speed of the car

Draw a free-body diagram for the car, and decompose all the forces acting on it into components that act parallel and perpendicular to the slope. The car moves parallel to the slope, so we only care about 2 forces: the parallel component of the car's weight, and the force provided by the engine.

By Newton's second law, since the car is moving at a constant speed,

F = F - m g sin(12°) = 0

where m = 950 kg and g = 9.80 m/s². Solve for F :

F = m g sin(12°) ≈ 1935.658 N

The engine provides P = 6.5 × 10⁴ W, so the car's speed v is

v = P / F = (6.5 × 10⁴ W) / (1935.658 N) ≈ 33.6 m/s

which makes C : 34 ms⁻¹ the closest answer.

User Derwrecked
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3.2k points