What is the correct way to find tension in a pulley problem?

In summary, the conversation discusses finding the acceleration and tension in a system of masses connected by strings and a pulley. The correct equations and steps are provided to solve for the acceleration and tension in each object. The tension in the ropes is found by subtracting the weight of the object from the sum of the forces on that object, taking into account the direction of the acceleration. The tension in the main string can be found by using the heaviest set of weights on either side of the pulley. The conversation concludes with a clarification of the calculations and a reminder to pay attention to signs.
  • #1
ja!mee
16
0
Okay So, the question I have here is..

Masses are connected as shown. m1 = 5.0 kg and m2 = 4.0 kg.
a) find the acceleration of each object and
b) the tension in the two strings

I have attached the picture example as well (as there is another unlisted weight in it) With pulley problem's I find it easier to find the acceleration first, so I have done so with:

a = Fg7- Fg5/Mt
a = (7kg)(9.8 m/s2) - (5kg)(9.8 m/s2) / 12 kg
where Fg7 is the force of gravity on the 4kg an 3 kg weigh combined and Fg5 is the force of gravity with the 5 kg weight.
I have found the the correct answer for question A) which is acceleration = 1.63

Now with that said an done I am not looking for the rope tension, I have my equation:

T = Fg7 - ma
T = 7 kg (9.8 + 1.6)
T = 79.8 N

Well that's all fine and dandy, but I am in a course where the answers are provided, it is the work that you do to get to the answer that really counts. The answer I have provided is not 79.8 N but 57N.

The only way I could see getting to this answer is
T = Fg5 - ma
T = 5 kg (9.8 + 1.6)
T = 57 N

It is my understanding that the tension equation that I take should come from the heaviest set of weights on any given side of the pulley. From the picture provided, you can see that there are two sets of weights on the one side of the pulley. Am I wrong in thinking that to find the tension I should add those two weights together and find the Tension from that number? Because this seems to contradict what the answer I have been provided is saying.

Or am I missing something completely?
 

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  • #2
ja!mee said:
Now with that said an done I am not looking for the rope tension, I have my equation:

T = Fg7 - ma
T = 7 kg (9.8 + 1.6)
T = 79.8 N
In the second step you added when you should have subtracted.

Better to do things systematically:
ƩF = ma
Taking up as positive, the acceleration is -1.63 m/s2:
T - mg = m(-1.63), and so on.

The only way I could see getting to this answer is
T = Fg5 - ma
T = 5 kg (9.8 + 1.6)
T = 57 N
Systematically:
ƩF = ma
Taking up as positive, the acceleration is +1.63 m/s2:
T - mg = m(1.63), and so on.

It is my understanding that the tension equation that I take should come from the heaviest set of weights on any given side of the pulley. From the picture provided, you can see that there are two sets of weights on the one side of the pulley. Am I wrong in thinking that to find the tension I should add those two weights together and find the Tension from that number? Because this seems to contradict what the answer I have been provided is saying.
You can use either side to find the tension, since it's the same. You just made an error with signs.
 
  • #3
Lookat m1 (5kg). You have its acceleration upwards =1.63. The forces acting on m1 are the upward force due to tension =T and the downward force due to its weight = 5 x 9.81
therefore for m1 resultant force (upward) T - 5x9.81 = 5 x 1.63
this gives T = 57.2N
For the string between m2 and the 3kg mass you need to look at the 3kg mass.
The 3kg mass is accel;erating down at 1.63 therefore the resultant force on the 3kg is (3 x 9.81) - tension
Therefore 29.43 - T = 3 x 1.63
gives T = 24.54N
 
  • #4
Thank you! that absolutely clears things up.
 
  • #5
You can check these numbers by looking at m2 (4kg)
It is accelerating down with acc = 1.63
The forces acting on m2 are the tension in the main string (57.2N upwards) with the weight (4x9.81) plus the tension in the other string (24.54) downwards.
therefore the resultant force downwards = 39.24 + 24.54 -57.2 = 6.58N
F = ma 6.58 = 4 x 1.63 (gives 6.52...sig figs)
 

1. 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 that runs over the wheel. It is used to lift or move heavy objects by reducing the amount of force needed to lift them.

2. How does a pulley work?

A pulley works by changing the direction of the force needed to lift an object. The rope or belt runs over the wheel, creating a mechanical advantage and reducing the amount of force needed to lift the object. The more pulleys used, the greater the mechanical advantage and the easier it is to lift the object.

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

A fixed pulley is attached to a stationary object and only changes the direction of the force, while a movable pulley is attached to the object being lifted and moves along with it, providing a greater mechanical advantage.

4. How does the number of pulleys affect the mechanical advantage?

The more pulleys used, the greater the mechanical advantage. This is because each additional pulley adds to the mechanical advantage by reducing the amount of force needed to lift the object.

5. What is the relationship between the load and the effort in a pulley system?

In a pulley system, the load is the weight of the object being lifted, while the effort is the force applied to lift the object. The relationship between the two is that the effort needed is equal to the load divided by the number of pulleys in the system.

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