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 1200 kg car is driven in sand at 5.2 m/s, the coefficient of rolling friction is 0.06. 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.
a) What propulsion force is needed to keep the car moving forward at a constant speed?
b) What power is required for propulsion at 5.2 m/s?
If the car gets 15 mpg when driving on sand, what is the car's efficiency? Assume the density of gasoline is 719.7 kg/m^3.
Help please!
a) F = M*g*0.06 = 705.6 N
b) Power = F*V
c) For efficiency, you need the heating value of the fuel as well as the mpg.
Fuel required to go one mile = 1/15 gallon = 0.257 liters = 2.57*10^-4 m^3
Mass of fuel needed per mile = 0.185 kg
Multiply that by the heat value for the chemical energy input.
The delivered power out per mile is F*1609 meters = 1.14*10^6 J
Efficiency = (mechanical work out)/(chemical energy in)
= ____
To find the propulsion force needed to keep the car moving forward at a constant speed, we need to consider the forces acting on the car. In this case, we can ignore air drag, so the only force we need to consider is the rolling friction.
a) The rolling friction force can be calculated using the equation:
rolling friction force = coefficient of rolling friction * normal force
The normal force is equal to the weight of the car, which can be calculated as:
weight = mass * gravitational acceleration
where the mass of the car is 1200 kg and the gravitational acceleration is approximately 9.8 m/s^2.
So the normal force is:
normal force = 1200 kg * 9.8 m/s^2
Now we can calculate the rolling friction force:
rolling friction force = 0.06 * (1200 kg * 9.8 m/s^2)
b) The power required for propulsion can be calculated using the formula:
power = force * velocity
Substituting the rolling friction force calculated in part a) and the given velocity of 5.2 m/s, we can calculate the power required for propulsion.
power = rolling friction force * velocity
To find the car's efficiency, we need to determine the rate at which it consumes fuel. Given that the car gets 15 mpg (miles per gallon) when driving on sand, we can calculate the fuel consumption rate using the formula:
fuel consumption rate = distance traveled / fuel used
Since we know the distance traveled (1 mile) and the fuel consumption rate (15 mpg), we can calculate the amount of fuel used.
fuel used = distance traveled / fuel consumption rate
Finally, to calculate the car's efficiency, we can use the formula:
efficiency = useful work / energy input
Since the car is using the energy from the fuel to overcome rolling friction, the useful work is equal to the power required for propulsion calculated in part b). The energy input can be calculated by multiplying the amount of fuel used by its energy content, which is given by the density of gasoline.
energy input = fuel used * density of gasoline
Now we can substitute the values into the formulas to find the required answers.
To solve this problem, we can use the equation for the force needed to overcome rolling friction and the equation for power. Let's break down each part of the problem step by step:
a) The propulsion force needed to keep the car moving forward at a constant speed can be calculated using the equation:
Force = Rolling Friction Coefficient * Normal Force
The normal force is the force exerted by the surface on the car, which in this case is equal to the weight of the car (mass * gravity).
Normal Force = Mass * Gravity
Since the problem states that the car has a mass of 1200 kg, we can substitute the values into the equation:
Force = Rolling Friction Coefficient * Mass * Gravity
Now we just need to calculate the force using the given values. The rolling friction coefficient is stated as 0.06, and the acceleration due to gravity is approximately 9.8 m/s^2.
Force = 0.06 * 1200 kg * 9.8 m/s^2
b) The power required for propulsion can be calculated using the equation:
Power = Force * Velocity
We already know the force from part (a), and the velocity is given in the problem as 5.2 m/s. Substitute the values into the equation:
Power = Force * Velocity
Now we can calculate the power using the force calculated in part (a) and the given velocity.
Power = Force * 5.2 m/s
For the efficiency part of the question, we need to first convert the fuel efficiency from miles per gallon (mpg) to meters per gallon:
1 mile = 1609.34 meters
To determine the distance covered in 1 gallon, we can multiply the fuel efficiency by this conversion factor:
Distance = Fuel Efficiency * 1609.34 meters
Then, we can calculate the energy consumed by the car in 1 gallon of gasoline:
Energy = Mass of Gasoline * Density of Gasoline * Energy Density of Gasoline
The energy density of gasoline is typically around 34.6 MJ/L. Assuming the density of gasoline given is in kg/m^3, we can calculate it by dividing by 1000:
Energy Density of Gasoline = 34.6 MJ/L * 1000 L/m^3 = 34,600,000 J/m^3
Finally, we can calculate the car's efficiency using the equation:
Efficiency = (Distance / Energy) * 100
Substitute the values we calculated earlier to determine the car's efficiency.