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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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In summary, the question is asking for the minimum work needed to push a 800 kg car 930 m up a 9.0^\circ incline. One way to approach this is by calculating the component of force (gravity) along the incline and multiplying it by the distance. Another way is to determine the change in gravitational potential energy over the distance and use that as the work. The minimum possible value of F can be found by multiplying the mass and gravity.

- #1

- 4

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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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- #2

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Hi cmed07! Welcome to PF!

(have a theta: θ and a degree: º )

First, what is the minimum possible value of F?

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There are a couple of ways to approach this. One way is to calculate the component of force (gravity) along (ie. parallel to) the [tex]9.0^\circ[/tex] 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.cmed07 said:

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?

AM

- #4

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

(have a theta: θ and a degree: º )

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...

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cmed07 said:That's all the information that was given to me...

D'oh!

To calculate the minimum work for an 800kg car on a 9.0° incline, you will need to use the formula W = mgh, where W is the work, m is the mass of the car, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the incline. In this case, the height of the incline can be calculated using the formula h = Lsinθ, where L is the length of the incline and θ is the incline angle (9.0° in this case).

The mass of the car used in the calculation is 800kg, as stated in the question. This is the value that should be substituted for the variable m in the formula W = mgh.

The length of the incline can be determined by measuring the distance from the starting point of the incline to the end point. Alternatively, if the incline is given as a height and angle, the length can be calculated using the formula L = h/sinθ.

The acceleration due to gravity, denoted by g, is a constant value of 9.8 m/s² on Earth. This value is used in the formula W = mgh to calculate the work done on an object due to the force of gravity.

Yes, this calculation can be used for any car on any incline, as long as the mass of the car and the angle of the incline are known. However, it is important to note that this calculation assumes ideal conditions and does not take into account factors such as friction and air resistance, which can affect the actual work done on the car.

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