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 amount of chemical energy needed to move the car a distance d at a constant speed, we need to consider the work done against the opposing force.
The work done (W) is given by the equation:
W = force x distance
In this case, the force acting against the car's motion is the frictional force, which is equal to 1.8 x 10^4 N. The distance the car moves is 450 m. Therefore, the work done is:
W = (1.8 x 10^4 N) x (450 m) = 8.1 x 10^6 J
However, we are given that the car's engine is only 12% efficient at converting chemical energy into mechanical energy. Therefore, only 12% of the chemical energy will be converted into mechanical energy, while the remaining energy is wasted as heat.
To find the amount of chemical energy needed, we can use the equation:
chemical energy = mechanical energy / efficiency
Substituting the values, we have:
chemical energy = (8.1 x 10^6 J) / 0.12 = 6.75 x 10^7 J
Therefore, approximately 6.75 x 10^7 Joules of chemical energy would be needed to move the car a distance of 450 m at a speed of 21 m/s.