How to Solve a Tension-Pulley Problem with Acceleration and Force

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In summary, the conversation discusses finding the force exerted by a rope on a bucket of water being raised from a well. The mass of the bucket is 9.4 kg and the acceleration of gravity is 9.8 m/s². The upward acceleration of the bucket is 2.8 m/s². The force is calculated by finding the weight of the bucket, which is 92.12 N, and then using that to find the tension in the rope, which is 118.44 N. The importance of labeling units, such as kg for mass and m/s² for acceleration, is also mentioned.
  • #1
Nemi
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I need advice on where to stick the ag

A (m1=9.4 kg) bucket of water is raised from a well by a rope. (ag=9.8 m/s²) If the upward acceleration of the bucket is (a=2.8 m/s²), find the force exerted by the rope on the bucket.

Finding Fw1
Fw1=m1(ag)
Fw1=(9.4 kg)(9.8 m/s²)
Fw1=92.12 N

Finding Tension
T-Fw1=m1(a)
T-92.12 N =(9.4 kg)(2.8 m/s²)
T=26.32+92.12
T=118.44 N

Am I doing good so far?
 
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  • #2
Real good. You have asked about what to do with the 'ag' (acceleration of gravity, usually just referred to as 'g'). Still wondering?
 
  • #3
Yes, but one should show units, e.g. (9.4 kg) for mass of bucket, (9.8 m/s2) for acceleration due to gravity and 2.8 m/s2 for acceleration of the bucket being pulled by the rope.

And for force, 1 N = 1 kg-m/s2.
 
  • #4
Thank you both, so much for your help. PhantomJay, thank you for your consideration, you helped me understand it now. Astronuc, I really appreciate your help in labeling my units.
 
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1. What is a tension-pulley problem?

A tension-pulley problem is a physics problem in which a system of pulleys and weights is analyzed to determine the tension in the pulley system and the forces acting on the objects involved.

2. How is tension calculated in a tension-pulley problem?

Tension is calculated by using the equation T = mg, where T is the tension force, m is the mass of the object, and g is the acceleration due to gravity. This equation can be used for each individual object in the system to determine the overall tension in the pulley system.

3. What are the different types of tension-pulley systems?

There are three main types of tension-pulley systems: fixed pulley systems, movable pulley systems, and combination pulley systems. Fixed pulleys have a stationary axle and are used to change the direction of a force. Movable pulleys have a movable axle and are used to multiply the applied force. Combination pulleys consist of a combination of fixed and movable pulleys and are used to both change direction and multiply force.

4. How do friction and the mass of the pulley affect tension in a tension-pulley problem?

Friction and the mass of the pulley can affect tension in a tension-pulley problem by introducing additional forces that need to be considered in the calculations. Friction can decrease the tension by opposing the motion of the pulley, while the mass of the pulley can increase the tension by adding to the overall weight of the system.

5. What are some real-world applications of tension-pulley problems?

Tension-pulley problems have many real-world applications, including elevator systems, cranes, and weightlifting machines. They are also used in engineering and construction to lift heavy objects and in the design of pulley systems for various machinery.

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