Calculating Min Work for 800kg Car on 9.0° Incline

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To calculate the minimum work required to push an 800 kg car up a 930 m incline at a 9.0° angle, the correct approach involves determining the gravitational force component acting along the incline. The formula W = Fdcos(θ) is relevant, but it's crucial to first find the height increase to compute the change in gravitational potential energy. This change in potential energy directly equates to the work done against gravity. The discussion highlights the importance of accurately calculating the force and understanding the relationship between distance, angle, and gravitational effects. Properly applying these principles will yield the correct minimum work value.
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I have been trying this problem multiple times but it still says I'm wrong:

What is the minimum work needed to push a 800 kg car 930 m up along a 9.0^\circ incline?

i'm using the formula:
W= Fdcos(theta)
F= mg

what am i doing wrong?
 
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Welcome to PF!

Hi cmed07! Welcome to PF! :smile:

(have a theta: θ and a degree: º :wink:)

First, what is the minimum possible value of F?
 
cmed07 said:
I have been trying this problem multiple times but it still says I'm wrong:

What is the minimum work needed to push a 800 kg car 930 m up along a 9.0^\circ incline?

i'm using the formula:
W= Fdcos(theta)
F= mg

what am i doing wrong?
There are a couple of ways to approach this. One way is to calculate the component of force (gravity) along (ie. parallel to) the 9.0^\circ inclined surface and multiply that force by the distance (930 m). The simpler way would be to determine the height increase over that 930 m and the resulting change in gravitational potential energy of the car. The work is equal to the change in gravitational potential energy.

AM
 


tiny-tim said:
Hi cmed07! Welcome to PF! :smile:

(have a theta: θ and a degree: º :wink:)

First, what is the minimum possible value of F?


That's all the information that was given to me... I know I'm supposed to find force by multiplying the mass and gravity...but i think the number I'm getting after i put it into the work formula is too big...
 
cmed07 said:
That's all the information that was given to me...

D'oh! :rolleyes:

On the information that was given to you, what is the minimum possible value of F? :smile:
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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