Power and Energy of a motor problem

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SUMMARY

The average power developed by a motor lifting a 400-kilogram mass through a vertical distance of 10.0 meters in 8.0 seconds is calculated using the formula P = W/t, where W is the work done. The work done is determined by the force exerted against gravity, which is equal to the weight of the mass (F = mg). Given that the acceleration is constant and equal to zero during the lift, the average power is conclusively 4900 W, as this is the only option that satisfies the equation when substituting the values for force and distance.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of work and power equations (P = W/t)
  • Familiarity with gravitational force calculations (F = mg)
  • Ability to interpret force diagrams and constant speed scenarios
NEXT STEPS
  • Study the derivation of power equations in physics
  • Learn about force body diagrams and their applications in mechanics
  • Explore the implications of constant speed on net force and acceleration
  • Investigate real-world applications of motor power calculations in engineering
USEFUL FOR

Students in physics, mechanical engineers, and anyone interested in understanding motor power calculations and the principles of work and energy in mechanical systems.

majormuss
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Homework Statement



What is the average power developed by a motor
as it lifts a 400.-kilogram mass at constant speed
through a vertical distance of 10.0 meters in
8.0 seconds?
(1) 320 W (3) 4,900 W
(2) 500 W (4) 32,000 W

Homework Equations



P=Wd/t= Fd/t= mad/t

The Attempt at a Solution


How does the fact that acceleration is 0 change the way I should approach this question. The question says acceleration is constant.
On the other hand I tried using this formula... P=Fv... but because I don't know acceleration, I can't find 'F'.
 
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The correct equation for power is: P=W/t

What is work? (W=Fd)
What is force? (F = ma)

In this problem, there are 2 accelerations to consider: (1) The problem says the speed is constant so the acceleration of the mass as it travels through space is 0. (2) assuming that this motor is operating near the surface of the Earth, the acceleration due to Earth's gravity is acting on the mass.
 
majormuss said:

Homework Statement



What is the average power developed by a motor
as it lifts a 400.-kilogram mass at constant speed
through a vertical distance of 10.0 meters in
8.0 seconds?
(1) 320 W (3) 4,900 W
(2) 500 W (4) 32,000 W

Homework Equations



P=Wd/t= Fd/t= mad/t

The Attempt at a Solution


How does the fact that acceleration is 0 change the way I should approach this question. The question says acceleration is constant.
On the other hand I tried using this formula... P=Fv... but because I don't know acceleration, I can't find 'F'.

Fv should work as well as wd/t, because d/t = v. To find the force, draw a force body diagram. What forces are acting on the 400kg object? Remember, force does not equal acceleration. A NET force equals an acceleration.
 

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