Question

Driving on asphalt roads entails very little rolling resistance, so most of the energy of the engine goes to overcoming air resistance. But driving slowly in dry sand is another story. If a 1300 kg car is driven in sand at 4.0 m/s , the coefficient of rolling friction is 0.060. In this case, nearly all of the energy that the car uses to move goes to overcoming rolling friction, so you can ignore air drag in this problem.

Part A

What propulsion force is needed to keep the car moving forward at a constant speed?

Express your answer with the appropriate units.

F

F

=

nothingnothing

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Part B

What power is required for propulsion at 4.0 m/s ?

Express your answer with the appropriate units.

P

P

=

nothingnothing

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Part C

If the car gets 15 miles per gallon when driving on sand, what is the car's efficiency? One gallon of gasoline contains 1.4×108 J of chemical energy, one mile is 1609 m.

Express your answer as a percentage.

Answer 1

A) as the car moving with constant speed, Fnet = 0

F_engine - f_rolling = 0

F_engine = f_rolling

= mue_r*N

= mue_r*m*g

= 0.06*1300*9.8

= 764.4 N <<<<<<<<----------------Answer

B) Power required, P = F*v

= 764.4*4

= 3058 W <<<<<<<<----------------Answer

C) Time taken to move 15 miles, t = d/v

= 15*1609/4

= 6034 s

Energy supplied by the engine during this time, E = Power*time

= 3058*6034

= 1.845*10^7 J

efficiency of car's engine, e = 1.845*10^7/(1.4*10^8)

= 0.132

= 13.2 % <<<<<<<<----------------Answer