How High Can a 12V Battery Lift an 8.1 kg Mass with a 90% Efficient Motor?

• pcandrepair
In summary, the conversation discusses a fully energized 12V battery with a rating of "4 Ampere-hours" and its use in powering a motor that is 90% efficient. The question is how high the motor can lift an 8.1 kg mass using the battery. Through the use of various equations, it is determined that the motor can do 155,520 joules of work, which can be used to find the maximum height the mass can be lifted, which is calculated to be approximately 1959.18 meters. This value is considered reasonable given the mass of the object.
pcandrepair

Homework Statement

A fully energized 12V battery is rated as "4 Ampere-hours." Suppose this battery is connected to a motor that is 90% efficient at converting electrical to mechanical power. How high could this battery-supplied motor lift a 8.1 kg mass?

V = I*R
P = V*I
P = (I^2)*R

The Attempt at a Solution

An amp-hour is how many amps a battery can supply for one hour.
Using the power equation:
P = (12V)*(4A*hr) = 48 Watt*hr

Since one watt-hr = 3600 Joules,
(48 W*hr)*(3600) = 1728 Joules

The motor is 90% efficient so,
1728 * .9 = 1555.2 Joules

I think the above is right (hopefully), but I'm not sure how to use the 1555.2 Joules to find the maximum height that this motor can lift the mass. Any help would be greatly appreciated. Thanks!

Power isn't in watt-hours, a watt hour is energy

Right idea still, 12V*4Ahr is 48 Watt*hr, but that itself equals 172800 joules

90% of that is straight up how much work the motor can do. Work...mass...looking for distance...

So, now at 90% of 172,800 J = 155,520 J

Using conservation of energy:
155,520 J = mgh
155,520 J = (8.1 kg)*(9.8 m/s^2)*(h)
h = 1959.18 m ?

This seems like a large value but reasonable because the mass is not that great.

Before I submit my answer, would you agree with using conservation of energy and the answer that I got?

1. What is the purpose of current in an electric motor?

Current is the flow of electric charge, and it is essential for the operation of an electric motor. The current provides the necessary energy for the motor to produce mechanical motion.

2. How does current affect the speed of an electric motor?

The current directly affects the speed of an electric motor because it determines the strength of the magnetic field that drives the motor's rotation. The higher the current, the stronger the magnetic field, and the faster the motor will spin.

3. Can the current be adjusted in an electric motor?

Yes, the current can be adjusted in an electric motor by varying the voltage supplied to the motor or by using a device called a motor controller. The current can also be adjusted by changing the size and type of the motor's windings or by adding external resistors.

4. What happens if too much current is supplied to an electric motor?

If too much current is supplied to an electric motor, it can overheat and potentially damage the motor's components. This is because the excess current produces more heat in the motor's windings, which can cause insulation breakdown and other failures.

5. How is the current converted into mechanical energy in an electric motor?

The current is converted into mechanical energy in an electric motor through the interaction of the motor's magnetic field and the electric current. As the current passes through the motor's windings, it creates a magnetic field that interacts with the permanent magnets or electromagnets in the motor's rotor, causing it to rotate and produce mechanical motion.

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