How long will it take a motor 1500 watt motor to lift a 500kg elevator 30 meters? Give your answer in minutes.
To calculate the time it takes for the motor to lift the elevator, we can use the equation:
\[ \text{{Work}} = \text{{Force}} \cdot \text{{Distance}} \]
The work done by the motor is equal to the power multiplied by the time:
\[ \text{{Work}} = \text{{Power}} \cdot \text{{Time}} \]
In this case, the power of the motor is given as 1500 watts, and the distance the elevator needs to be lifted is 30 meters. We need to calculate the time it takes for the elevator to be lifted.
First, we need to find the force required to lift the elevator. The force is given by the equation:
\[ \text{{Force}} = \text{{mass}} \cdot \text{{gravity}} \]
The mass of the elevator is given as 500 kg, and the acceleration due to gravity is approximately 9.8 m/s\(^2\). Substituting these values into the equation, we get:
\[ \text{{Force}} = 500 \, \text{{kg}} \times 9.8 \, \text{{m/s}}^2 \]
Now, we can substitute the force and distance into the first equation to solve for work:
\[ \text{{Work}} = \text{{Force}} \times \text{{Distance}} \]
\[ \text{{Work}} = (\text{{Force}}) \times (\text{{Distance}}) = (500 \, \text{{kg}} \times 9.8 \, \text{{m/s}}^2) \times 30 \, \text{{m}} \]
Finally, we can use the work and power equations to find the time:
\[ \text{{Work}} = \text{{Power}} \times \text{{Time}} \]
\[ \text{{Time}} = \frac{{\text{{Work}}}}{{\text{{Power}}}} = \frac{{(500 \, \text{{kg}} \times 9.8 \, \text{{m/s}}^2) \times 30 \, \text{{m}}}}{{1500 \, \text{{W}}}} \]
Simplifying the equation, we can cancel out units and calculate the time in minutes:
\[ \text{{Time}} = \frac{{500 \, \text{{kg}} \times 9.8 \, \text{{m/s}}^2 \times 30 \, \text{{m}}}}{{1500 \, \text{{W}}}} \times \frac{{60 \, \text{{s}}}}{{1 \, \text{{min}}}} \]
\[ \text{{Time}} = \frac{{500 \times 9.8 \times 30 \times 60}}{{1500}} \, \text{{mins}} \]
Simplifying the equation, we get:
\[ \text{{Time}} = 588 \, \text{{mins}} \]
So, it will take approximately 588 minutes for the 1500-watt motor to lift the 500 kg elevator a distance of 30 meters.