A car's engine is only 12% efficient at converting chemical energy in gasoline into mechanical
energy. If it takes 1.8 x 104 N of force to keep the car moving at a constant speed of 21 m/s,
how much chemical energy would be needed to move the car a distance of 450 m at this speed?
To find the chemical energy needed to move the car a distance of 450 m at a constant speed of 21 m/s, we need to first determine the work done on the car.
Work (W) is given by the formula:
W = force x distance
Given:
Force (F) = 1.8 x 10^4 N
Distance (d) = 450 m
W = F x d
W = 1.8 x 10^4 N x 450 m
W = 8.1 x 10^6 Nm
Next, we need to find the amount of mechanical energy produced by the car's engine. The engine is only 12% efficient at converting chemical energy into mechanical energy. Therefore, the mechanical energy produced (E) can be expressed as:
E = W / efficiency
Given:
Efficiency (η) = 12% = 0.12
E = 8.1 x 10^6 Nm / 0.12
E = 6.75 x 10^7 Nm
Since the mechanical energy produced is equal to the chemical energy needed, the amount of chemical energy needed to move the car a distance of 450 m at a constant speed of 21 m/s is 6.75 x 10^7 Nm.
To find out how much chemical energy is needed to move the car a distance of 450 m at a constant speed of 21 m/s, we need to calculate the total work done by the car.
Work is defined as the product of force and displacement: Work = Force × Distance × cos(θ)
In this case, the car is moving at a constant speed, so the angle (θ) between the force and displacement is 0 degrees. Therefore, the expression simplifies to:
Work = Force × Distance
To calculate the force, we can use Newton's second law of motion, which states that Force = Mass × Acceleration. Since the car is moving at a constant speed, there is no acceleration, so the force can be calculated as:
Force = Mass × Acceleration = Mass × 0 = 0 N
However, we are given that it takes 1.8 x 10^4 N of force to keep the car moving at a constant speed of 21 m/s. This means that there must be some other force acting in the opposite direction to balance out the force we calculated.
The force acting in the opposite direction is due to friction. Friction opposes the motion of the car and requires additional force to maintain the constant speed. Therefore, the force required to keep the car moving is 1.8 x 10^4 N.
Now, we can calculate the work done by the car:
Work = Force × Distance = (1.8 x 10^4 N) × (450 m)
The work done by the car represents the mechanical energy that is needed to overcome the force of friction and move the car a distance of 450 m. However, the car's engine is only 12% efficient at converting chemical energy into mechanical energy. Therefore, the work done by the car's engine is only 12% of the total mechanical energy needed.
To find out the total chemical energy needed, we can use the formula:
Total Chemical Energy = Work done by the car's engine ÷ Efficiency
Total Chemical Energy = (1.8 x 10^4 N) × (450 m) ÷ 0.12
By calculating the above expression, we can find the total chemical energy needed to move the car a distance of 450 m at a constant speed of 21 m/s.