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?
chemenergy=1.8E4*450m/.12
6.7 x 10^7
To find the amount of chemical energy needed to move the car a distance of 450 m at a speed of 21 m/s, we can use the formula for work, which is given by:
Work = Force x Distance
First, let's calculate the work done on the car to keep it moving at a constant speed of 21 m/s:
Work = Force x Distance
= (1.8 x 10^4 N) x (450 m)
= 8.1 x 10^6 N·m
Now, let's find the mechanical energy needed to move the car this distance. Since the engine is only 12% efficient, we need to account for the efficiency:
Mechanical energy = Work / Efficiency
= (8.1 x 10^6 N·m) / 0.12
= 6.75 x 10^7 N·m
Hence, the amount of chemical energy needed to move the car a distance of 450 m at a speed of 21 m/s is 6.75 x 10^7 N·m.
To find the amount of chemical energy needed to move the car a distance of 450 meters at a constant speed, we can use the concept of work and energy.
First, let's find the work done by the force to keep the car moving. Work is defined as the product of force and displacement.
Work (W) = Force (F) x Displacement (d) x cos(theta)
In this case, since the car is moving at a constant speed, the angle between the applied force and the displacement is 0 degrees. Therefore, the work equation simplifies to:
Work (W) = Force (F) x Displacement (d)
Now, substitute the given values into the equation:
Work = (1.8 x 10^4 N) x (450 m)
= 8.1 x 10^6 N*m
The unit N*m is also known as Joules (J). So, the work done by the force is 8.1 x 10^6 J.
Next, we need to calculate the total energy required to overcome the car's inefficiency. The engine efficiency is given as 12%, which means only 12% of the chemical energy is converted into mechanical energy. Therefore, we need to find the total chemical energy required.
Total chemical energy = Work done / Efficiency
Total chemical energy = (8.1 x 10^6 J) / 0.12
= 6.75 x 10^7 J
Therefore, the amount of chemical energy needed to move the car a distance of 450 meters at a speed of 21 m/s is approximately 6.75 x 10^7 Joules.