Finding work done by a escalor

In summary, the conversation discusses the process of finding the amount of work done on a mass by using Newton's second law and the formula for work. The individual calculated the force on the mass to be 559.58 N and used the formula Work = Fcos(theta)D to find the work to be 31896.37 J. However, they question the use of cosine and suggest using sine instead. They also mention a similar problem and wonder if the formula for work should be Fsin(theta)D instead.
  • #1
sylavel
5
0

Homework Statement


http://img252.imageshack.us/my.php?image=heyheygw0.jpg
Mass=57.1 Kg
Distance 69.5 m
G= 9.8
Theta= 34.9
So I'm trying to find the amount of work done on mass.

Homework Equations


F=ma
Work=Fcos(theta)D

The Attempt at a Solution


Okay so i started out finding Force by Newtons 2nd law.
F=ma
f=57.1(9.8)
F=559.58
Okay so then I went with force to the work fomula.
Work=559.58cos(34.9)69.5
and that gave me 31896.37
but this answer proved to be incorrect?
 
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  • #2
Why cos(theta)? Over what height is mass (or weight) lifted?
 
  • #3
good question.
sin would prehaps be more fitting =)
 
  • #4
I have a similar problem like this so if I was to solve this problem would it go like this:
Work=Fsin(theta)D

?
 
  • #5


I would first check the unit of the final answer to ensure that it is in Joules (J), the unit for work. In this case, the units do not match, so there must be an error in the calculation.

Upon closer inspection, it seems that the calculation for force was incorrect. It should be F=57.1(9.8*cos(34.9)), since the force is acting at an angle to the horizontal. By using the cosine function, we can find the component of the force in the horizontal direction.

Plugging in the correct value for force, we get Work=57.1(9.8*cos(34.9))*69.5= 31600.55 J. This is the correct answer for the work done by the escalator on the mass.
 

1. What is the definition of work done by an escalator?

The work done by an escalator is the transfer of energy from the motor of the escalator to the passengers riding on it. This energy is used to move the passengers and their belongings up or down the escalator.

2. How is the work done by an escalator calculated?

The work done by an escalator can be calculated by multiplying the force of gravity (9.8 m/s^2) by the mass of the passengers and their belongings, and then multiplying that by the height that the escalator has moved them.

3. Is the work done by an escalator positive or negative?

The work done by an escalator is typically considered positive, as it is providing energy to move the passengers and their belongings. However, if the escalator is moving downwards and the passengers are resisting that motion, the work done can be considered negative.

4. How does the work done by an escalator compare to other forms of work?

The work done by an escalator is similar to other forms of work, such as lifting an object by hand or using a pulley system. However, the difference is that the work done by an escalator is primarily done by a machine, rather than by human effort.

5. Can the work done by an escalator be changed?

Yes, the work done by an escalator can be changed by adjusting the speed and direction of the escalator's motor. Increasing the speed or changing the direction of the escalator will increase the work done, while decreasing the speed or changing the direction will decrease the work done.

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