A 500 kg car has an engine that uses only 40% of the energy from the gasoline for motion. If there is 15,000J of potential energy stored in the gasoline, how fast an the car go on the gasoline?
I have no idea how to set this up. Any help?!
It is a silly problem, I guess it wants you to ignore road friction, change of elevation, and air friction. If we could do that, it would be very inexpensive to drive. One could drive from LAngeles to SanDiego for no cost.
15000*.4= 1/2 mass*velocity^2
solve for veloctiy
To solve this problem, we can use the concept of energy conservation. The potential energy stored in the gasoline is converted into kinetic energy, which is responsible for the car's motion.
Step 1: Find the total amount of energy available from the gasoline.
You are given that there is 15,000 J of potential energy stored in the gasoline.
Step 2: Determine how much energy is used by the car's engine.
It is mentioned that the car's engine only uses 40% of the energy from the gasoline for motion. We need to find the amount of energy used by the engine.
Total energy = Energy used by the engine + Energy not used by the engine
Since the engine only uses 40% of the energy, it means that 60% is not used. Therefore:
Total energy = 40% + 60% = 100%
Step 3: Calculate the energy used by the engine.
Multiply the total energy by the percentage used by the engine:
Energy used by the engine = Total energy * Percentage used by the engine
Energy used by the engine = 15,000 J * 40% = 6,000 J
Step 4: Convert the energy used by the engine into kinetic energy.
Kinetic energy = Energy used by the engine
Step 5: Apply the formula for kinetic energy.
The formula for kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2
Given mass (m) of the car = 500 kg
Given kinetic energy (K.E.) = 6,000 J
Rearrange the formula to solve for velocity:
velocity = sqrt((2 * K.E.) / m)
Substitute the known values:
velocity = sqrt((2 * 6,000 J) / 500 kg)
Solve the equation to find the velocity.
velocity = sqrt(24 J / kg)
Therefore, the car can go at a speed of approximately 4.9 m/s when using the energy from the gasoline.