Calculate Work on Trunk going up Incline

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In summary, a 1.8 kg trunk is pushed 62 cm up an incline with an angle of inclination of 24.0° by a constant horizontal force of 375 N. The coefficient of kinetic friction between the trunk and the incline is 0.19. The work done on the trunk by the applied force P is 212 J, and the work done by the frictional force is 19.9 J. The work done on the trunk by the gravitational force (its weight) depends on the displacement of the trunk in the direction of its weight and can be either positive or negative.
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Homework Statement


A trunk of mass m = 1.8 kg is pushed a distance d = 62 cm up an incline with an angle of inclination θ = 24.0° by a constant horizontal force P = 375 N (see figure). The coefficient of kinetic friction between the trunk and the incline is 0.19.
Figure: img144.imageshack.us/img144/8295/prob13ani7.gif

A) Calculate the work done on the trunk by the applied force P.
B) Calculate the work done on the trunk by the frictional force.
C) Calculate the work done on the trunk by the gravitational force.

Homework Equations


sin θ = y/h
cos θ = x/h
N*μk=Fk

The Attempt at a Solution


A)
cos(θ)*F*h
cos(24°)*375N*0.62m = 212J

B)
N*μk=Fk
(sin(24°)*375N + cos(24°)*1.8kg*9.8m/s/s)*.62m*.19 = 19.9J

C)
This is where I am having problems.
 

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  • #2
Hi, Bartman, welcome to PF!

The work done by a force is equal to the product of the force times the displacement in the direction of the force ((F)(d)(cos theta)), where theta is the angle between the force and the displacement, and which can result in a positive or negative value. In part B, is the work done by friction positive or negative? In part C, the work done by the gravitational force is the work done by the trunk's weight. What is the displacement of the trunk in the direction of its weight? Is the work done by gravity positive or negative?
 
  • #3
I am not sure how to calculate the work done by the gravitational force. I know that work is equal to force multiplied by distance, but I am not sure how to incorporate the angle of inclination into this calculation. I would appreciate any guidance on how to approach this problem.

To calculate the work done by the gravitational force, we can use the formula W = mgh, where m is the mass of the trunk, g is the acceleration due to gravity (9.8 m/s^2), and h is the height the trunk is lifted.

We can find the height by using the trigonometric relationship sin θ = y/h, where y is the vertical displacement of the trunk and h is the height. Since we are pushing the trunk up the incline, y = d*sin θ (where d is the distance the trunk is pushed up the incline).

So, the work done by the gravitational force would be:
W = (1.8 kg)*(9.8 m/s^2)*(0.62 m*sin 24°) = 6.9 J

Therefore, the total work done on the trunk is:
W = 212 J + 19.9 J + 6.9 J = 238.8 J

 

What is the formula for calculating work on a trunk going up an incline?

The formula for calculating work on a trunk going up an incline is W = mghsinθ, where W is the work done, m is the mass of the trunk, g is the acceleration due to gravity, h is the height of the incline, and θ is the angle of the incline.

How do you determine the angle of the incline?

The angle of the incline can be determined by measuring the height and length of the incline and using the formula θ = tan⁻¹(h/l), where θ is the angle of the incline, h is the height of the incline, and l is the length of the incline.

What is the unit of measurement for work?

The unit of measurement for work is the joule (J), which is equivalent to a Newton-meter (N·m).

How does the mass of the trunk affect the work done?

The mass of the trunk directly affects the work done. The greater the mass, the more work is required to move the trunk up the incline. This can be seen in the formula W = mghsinθ, where the mass (m) is a factor in the calculation of work.

Does the direction of the incline affect the work done on the trunk?

Yes, the direction of the incline does affect the work done. If the trunk is moving up the incline, work is being done against the force of gravity. If the trunk is moving down the incline, the force of gravity is aiding in the movement and less work is required. This can be seen in the formula W = mghsinθ, where the angle (θ) is a factor in the calculation of work.

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