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 1500 kg car is driven in sand at 4.9 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.

Required:
a. What propulsion force is needed to keep the car moving forward at a constant speed?
b. What power is required for propulsion at 5.0 m/s?
c. If the car gets 15 mpg when driving on sand, what is the car's efficiency? One gasoline contains 1.4×10 ^8 J of chemical energy.

Answer 1

a)
`F_p=882N`

b)
`P=4410W`

c)
`V_p'=24135` ,
`n=15.2\%`

Step-by-step explanation:

From the question we are told that:

Mass
`M=1500kg`

Velocity
`v=4.9m/s`

Coefficient of Rolling Friction
`\mu=0.06`

a)

Generally the equation for The Propulsion Force is mathematically given by

`F_p=\mu*mg`

`F_p=0.06*1500*9.81`

`F_p=882N`

b)

Therefore Power Required at

`V_p=5.0m/s`

`P=F_p*V_p`

`P=882*5`

`P=4410W`

c)

`V_p' =15mpg`

`V_p'=15*\frac{1609}`

`V_p'=24135`

Generally the equation for Work-done is mathematically given by

`W=F_p*V_p'`

`W=882*15*1609`

`W=2.13*10^7`

Therefore

Efficiency

`n=(W)/(E)*100\%`

Since

Energy in one gallon of gas is

`E=1.4*10^8J`

Therefore

`n=(2.1*10^7)/(1.4*10^8)*100\%`

`n=15.2\%`