Finding work done by friction on a box

In summary, a box with a mass of 59.0 kg is pushed a distance of 83.0 m across a rough warehouse floor by an applied force of 204 N at an angle of 30.0° below the horizontal. The coefficient of kinetic friction is 0.100. To determine the work done by the force of friction, the equations W = fdcosΘ and Fƒ=μN were used. However, it was found that the normal force is larger than the weight, causing the vertical component of the applied force to add to the weight. This results in the wrong answer and further calculations are needed.
  • #1
99gray
1
0
1.
A box of mass
m = 59.0 kg
(initially at rest) is pushed a distance
d = 83.0 m
across a rough warehouse floor by an applied force of
FA = 204 N
directed at an angle of 30.0° below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.100. Determine the work done by the force of friction
7-p-001.gif


Homework Equations


W = fdcosΘ
Fƒ=μN

The Attempt at a Solution


I used the two above equations and I found that the applied force of friction would be 57.82 because that is .1*59*9.8 and then if you put that into the first equation, the work would be 57.82*83*cos30 which equals 4156.108 and then since it is opposite the applied force, it would be -4156.108. At least I thought. That's wrong and I don't know why. Please help!
 
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  • #2
But in this problem, the normal force is larger than the weight.
 
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  • #3
The vertical component of F add to weight.
Remember when resolving vector, here force, noted all the components. Here the X and Y components.
 

Related to Finding work done by friction on a box

1. What is friction and how does it affect the work done on a box?

Friction is a force that opposes motion between two surfaces in contact. In the context of a box, friction occurs between the box and the surface it is resting on. Friction can either increase or decrease the work done on a box, depending on the direction of the movement and the coefficient of friction between the surfaces.

2. How is the work done by friction on a box calculated?

The work done by friction on a box can be calculated by multiplying the force of friction by the distance the box travels in the direction of the force. This can be represented by the equation W = Ff * d, where W is the work done, Ff is the force of friction, and d is the distance traveled.

3. What factors affect the work done by friction on a box?

The work done by friction on a box is affected by the coefficient of friction, the weight of the box, and the distance the box travels. The coefficient of friction is a measure of how rough or smooth the surface is, and a higher coefficient of friction will result in a greater amount of work done by friction.

4. How does the angle of incline affect the work done by friction on a box?

If a box is placed on an incline, the work done by friction will be affected by the angle of the incline. As the angle of incline increases, the force of friction will also increase, resulting in a greater amount of work done by friction on the box.

5. Can work be done by friction on a box if the box is not moving?

Yes, work can still be done by friction on a box even if the box is not moving. This is because friction is a force that acts in the opposite direction of motion, and it requires energy to overcome this force. Therefore, even if the box is not moving, energy is still being used to maintain its position against the force of friction, resulting in work being done on the box.

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