Calculating Acceleration in a Pulley System

In summary, the problem involves a man weighing 80 kg exerting a force of 200N on a 40 kg dumb-waiter in a pulley system. The acceleration of the dumb-waiter is determined to be -0.2 m/s^2 based on the given information. The solution of 0.2 m/s^2 in the textbook may be rounded off and the actual answer is -0.2 m/s^2.
  • #1
eno
7
0
PLZ HELP! I am puzzled with this problem, and all i could find are that the forces equal, but the ans int eh back of the textbook clearly says the solution is 0.2 m/s2

Question: This situation occurs in a pulley system. A 80.0 kg man inside a 40.0 kg dumb waiter (like an elevator) pulls down on the rope. At the end of the rope, it is attached to the dumb-waiter. At the other end, the person exerts a force. At that moment, the scale on which he is standing reads 200N. Determine the elevator's acceleration.

THX for ur time!
 
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  • #2
Hmm.. that's wierd. I didn't get 0.2m/s^2

Let me try to understand this better. The man is inside the dumbwaiter (which will pull up the elevator) has a mass of 80kg, the dumbwaiter is 40kg, so total mass of the dumbwaiter is 120kg. Correct?


http://img52.exs.cx/img52/1381/2035.gif


I got 8.1 m/s^2 as an answer. So I don't know if I'm wrong, or the book is.
 
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  • #3
MAYBE this is the correct answer:
[tex]80+40=120[/tex]

[tex](120)(9.8)=1176[/tex]

[tex]F=MA[/tex]

[tex]A=\frac{F}{M}[/tex]

[tex]A=\frac{200}{1176}[/tex]

[tex]A=0.17m/s^2[/tex]
Probably the 0.17 is rounded off.
 
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  • #4
sorry, Raza, nice try. the 1176 is the force, and not the mass, so u cannot use the force of 200N to divide that force, which results in some unknown unit number. THe answer just conincidently matches with the ans int he book, but i am sure the way u got it is wrong...again, thanks for trying.

physik, here's the link to the actual question and diagram from the textbk:

http://www.enovon.com/public/physics.jpg

again, thanks for trying, maybe u can understand the problem better by this clear picture :)
 
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  • #5
Let us consider the dumb-waiter separately.
The man standing on it has a mass 80 kg, but the force exerted by him on the elevator is 200N.
He is applying some force on the rope, say F.
80g-F=200
You can solve this to know F.
Now the weight of the elevator is 40 kg ang the force exerted by the man is 200N. Let the acc. of the elevator be a.
F-200-40g=40a.
Substituting F=80g-200
we get 80g-200-200-40g=40a
Therefore,40g-400=40a
Therefore,a=g-10,
Therefore,a=-0.2m/s^2
That is 0.2 m/s^2 downwards
 
  • #6
thx alot, gauravkukreja!
 

What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or belt wrapped around it. It is used to change the direction of a force and to reduce the amount of force needed to lift an object.

How does a pulley work?

A pulley works by distributing the weight of an object over multiple ropes or belts. By distributing the weight, it reduces the amount of force needed to lift the object. When one end of the rope is pulled, the wheel turns and the object is lifted.

What is the difference between a fixed pulley and a movable pulley?

A fixed pulley has an axle attached to a fixed point, while a movable pulley has an axle that is free to move. A fixed pulley only changes the direction of the force, while a movable pulley also reduces the amount of force needed to lift an object.

What is mechanical advantage?

Mechanical advantage is a measure of how much a machine multiplies the force applied to it. In the case of a pulley, mechanical advantage is calculated by dividing the weight of the object by the force needed to lift it. The more ropes or belts are used in a pulley system, the greater the mechanical advantage.

How do I calculate the mechanical advantage of a pulley system?

To calculate the mechanical advantage of a pulley system, you need to count the number of ropes or belts that support the object being lifted. Each supporting rope or belt adds one to the mechanical advantage. For example, a system with two ropes supporting the object would have a mechanical advantage of 2.

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