Calculating Winch Power for an Inclined Ore Car: 30 Degree Incline | 950kg Mass

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To calculate the power required by the winch motor for a 950kg ore car on a 30-degree incline, the tension in the rope must be determined. The gravitational force component opposing the tension was calculated using the sine function, resulting in a force of approximately 4.9 N. Power is then calculated as the product of this force and the constant speed of 2.2 m/s, yielding a result of 10.78 W, which is significantly lower than the book's answer of 10.2 kW. The confusion arises from the unit conversion, as the calculated power should be in watts rather than kilowatts. Proper understanding of the force components and unit conversions is essential for accurate calculations.
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Homework Statement


A loaded ore car has a mass of 950kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0 degrees above the horizontal. The car accelerates uniformly to a speed of 2.2 m/s in 12.0 seconds and then continues at a constant speed.

a) what power must the winch motor provide when the car is moving at constant speed?


Homework Equations


Well, Power=Force x Velocity
Force = T

The Attempt at a Solution


Well to find the Tension in the rope, I found the component of G that was opposite the Tension and set it to -Fs. Then I set -Fs + T = 0 => Fs = T. Looking at The triangle under the cart I used sin(30)= Fs/g => Fs= gsin(30) which = 4.9 N

Since power = F*V I got P= (4.9)(2.2) = 10.78 kW. The back of the book says its 10.2 kW though. I am just wondering where I went wrong
 
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cooltee13 said:
Well to find the Tension in the rope, I found the component of G that was opposite the Tension and set it to -Fs. Then I set -Fs + T = 0 => Fs = T. Looking at The triangle under the cart I used sin(30)= Fs/g => Fs= gsin(30) which = 4.9 N

I can't understand what you do with Fs and T. You do not use the mass of the cart. 4.9 N * 2.2 m/s will give you 10.78 W and not 10.78 kW
 
Oh ok, well then care to give me some advice on how to solve the problem then?
 
cooltee13 said:
Oh ok, well then care to give me some advice on how to solve the problem then?

The Idea of splitting the force of gravity in components parallel and perpendicular to the ground was ok. As was power = force * speed
 
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