Work, Energy and Power (Work Problem)

In summary: Thanks so much for your help.In summary, the man has done work against friction of 1732J, and against gravity of 4450J.
  • #1
matadorqk
96
0

Homework Statement


A man drags a sack of flour of mass 50kg at a constant speed up an inclined plane to a height of 5.0m. The plane makes an angle of 30 degrees with the horizontal, and has a constant frictonal force of 200N, which acts on the sack down the plane. Calculate the work the man has dne against the friction, and against gravity.

Homework Equations


[tex]W=(F)(S)[/tex] (Where f=force and s=displacement)
[tex]W=(F\cos\vartheta)(S)[/tex]
**Also usage of SOHCAHTOA to solve the triangle.

The Attempt at a Solution



Well, first I drew a triangle for the problem, and obtained that he travels a total of 10m going upward 30 degrees to the horizontal.
Therefore, I solved it like this:
Against friction, the force is 200N, so (200cos30)(10) = 1732J.
Against gravity, the force is (50)(9.8) so (490cos30)(10)=4244J.

**I am unclear overall if I am doing this right, some help?
 
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  • #2
As I further tried solving, wouldn't the work done against gravity be the following:

[tex]W_{g}=mgh=(50)(9.8)(5)=2450J[/tex]

? Any ideas?
 
  • #3
matadorqk said:
As I further tried solving, wouldn't the work done against gravity be the following:

[tex]W_{g}=mgh=(50)(9.8)(5)=2450J[/tex]

? Any ideas?
Yep, that's correct, nice job. Now, calcualte the work done against friction. HINT: How much work is done by the friction force?
 
  • #4
PhanthomJay said:
Yep, that's correct, nice job. Now, calcualte the work done against friction. HINT: How much work is done by the friction force?

The friction force does a force of 200N. So, if we plot that into our equation for work, its
W=200s, but its an inclined plane, so the W=(200cos30)(s), where s=10, so when I solve for work, I get that is 1732J, is that right?
 
  • #5
matadorqk said:
The friction force does a force of 200N. So, if we plot that into our equation for work, its
W=200s, but its an inclined plane, so the W=(200cos30)(s), where s=10, so when I solve for work, I get that is 1732J, is that right?
No. You are correct that s=10. You are also correct that the friction force is 200N. And you are also corect tnat the work done by the friction force is 200s.. But then you incorrectly throw cos 30 in there. Remember that work is force times distance in the direction of the force.
 
  • #6
PhanthomJay said:
No. You are correct that s=10. You are also correct that the friction force is 200N. And you are also corect tnat the work done by the friction force is 200s.. But then you incorrectly throw cos 30 in there. Remember that work is force times distance in the direction of the force.

Ohh, so the frictional force is solely pushing downwards on the sack, therefore meaning that the frictional force is an upward force, so the frictional force of the object would be 2000J?
 
  • #7
matadorqk said:
Ohh, so the frictional force is solely pushing downwards on the sack, therefore meaning that the frictional force is an upward force, so the frictional force of the object would be 2000J?
Oh, now your mixing up your directions. Yes the friction force is down the plane. It is not an upward force, it is a downward force. So the man is exerting an upward force to counteract it (and gravity). 2000J is correct for the work done by the man against friction. So what is the total work done by the man against friction and gravity??
 
  • #8
PhanthomJay said:
Oh, now your mixing up your directions. Yes the friction force is down the plane. It is not an upward force, it is a downward force. So the man is exerting an upward force to counteract it (and gravity). 2000J is correct for the work done by the man against friction. So what is the total work done by the man against friction and gravity??

Well, he does 2000J against friction, and 2450J against gravity, for a total work of 4450J.
 
  • #9
matadorqk said:
Well, he does 2000J against friction, and 2450J against gravity, for a total work of 4450J.
Yup, that'll do it.
 
  • #10
PhanthomJay said:
Yup, that'll do it.

Thanks so much for your help.
 

1. What is the definition of work?

Work is defined as the transfer of energy that occurs when a force is applied to an object and the object is moved in the direction of the force.

2. How is work calculated?

Work is calculated by multiplying the force applied to an object by the distance the object moves in the direction of the force. The formula for work is W = Fd, where W is work, F is force, and d is distance.

3. What is the unit of measurement for work?

The unit of measurement for work is joule (J) in the International System of Units (SI). In the British system, work is measured in foot-pounds (ft-lb).

4. What is the difference between work and power?

Work and power are related concepts but have different meanings. Work is the transfer of energy, while power is the rate at which work is done. In other words, power is the amount of work done per unit of time. The formula for power is P = W/t, where P is power, W is work, and t is time.

5. How is work related to energy?

Work and energy are closely related concepts. Work is a transfer of energy, meaning that work is done when energy is transferred from one object to another. In other words, work is a measure of energy. The more work is done, the more energy is transferred.

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