A 500 kg dragster reaches a speed of 100 m/s on level ground, starting from rest. Its efficiency is only 8.00% in producing kinetic energy, because of friction and its design for high power without regard to efficiency.

(a) How many gallons of fuel does it use during this acceleration, given there are 1.30 multiplied by 108 J of energy per gallon?

(b) How much waste heat is produced?

(c) Once it is brought back to rest (assuming the engine shuts off at the end of the race), how much waste heat has been produced?

Someone help me to solve the problem.Please give me the steps.Thank you very much.

Eric/Alice/Amy -- please use the same name for your posts.

KE of dragster: 1/2 m v^2 solve that.

Energy input=KEdragster/.080

energy input=1.30*108J*volume
set them equal, solve for volume
waste heat=energy input-KE or
waste heat=energy input*.92

To solve this problem, we need to follow a few steps. Here's a step-by-step approach to finding the answers to each part of the problem:

(a) To calculate the amount of fuel used during the acceleration, we need to find the total amount of energy required and then convert it into gallons of fuel. The total energy required can be calculated using the formula:

Energy = (1/2) * mass * velocity^2

Given:
Mass = 500 kg
Velocity = 100 m/s

Plugging these values into the formula, we have:
Energy = (1/2) * 500 kg * (100 m/s)^2

Now we multiply this energy by the efficiency (8.00%) to account for the losses due to friction and design. To do this, we multiply the energy by 0.08:

Energy_Used = Energy * 0.08

Next, we need to convert this energy into gallons of fuel using the conversion factor given: 1.30 x 10^8 J/gallon. We can use the following equation:

Fuel_Used (in gallons) = Energy_Used / (1.30 x 10^8 J/gallon)

(b) To find the waste heat produced during the acceleration, we need to subtract the final kinetic energy from the total energy used. The waste heat is the remaining energy that was not converted into kinetic energy. We can calculate the final kinetic energy using the formula:

Final_Kinetic_Energy = (1/2) * mass * (Velocity_final)^2

Given:
Mass = 500 kg
Velocity_final = 100 m/s

Plugging in these values, we have:
Final_Kinetic_Energy = (1/2) * 500 kg * (100 m/s)^2

Now the waste heat can be calculated as:
Waste_Heat = Energy_Used - Final_Kinetic_Energy

(c) If the engine shuts off at the end of the race, we assume that no additional energy is consumed, and the only waste heat produced is from the race itself. Therefore, the waste heat produced when the dragster is brought back to rest will be the same as the waste heat calculated in part (b), which is:

Waste_Heat_Rest = Waste_Heat

Now you can substitute the values into the appropriate formulas and calculate the answers to each part of the problem.