Tension in Chain in Multiple Pulley Station

[magnumxlv]

This is for a graded online homework due at 11. I got everything else on it right, but this is giving me trouble for some reason. We get to resubmit answers once, and my first answer of 215.6N was wrong

Question: The pulley system in the figure is used to lift a crate of mass m = 44 kg. Note that a chain connects the upper pulley to the ceiling and a second chain connects the lower pulley to the crate. Assume that the masses of the chains, pulleys, and ropes are negligible. Determine the tension in each chain when the crate is being lifted with constant speed.

Diagram: https://jshare.johnshopkins.edu/amian3/public_html/pulleysystem.gif?uniq=-25jd0a

Initially, I figured the weight of the object would be distributed by the 2 tensions to the ceiling so I answered mg/2 which was 44*9.8/2 = 215.6N.

If anyone could help me out it'd be much appreciated, thank you.

 

[magnumxlv]

Figured it out. It's just m*g = 431.2N. The Tension of the rope to the ceiling and the pulling force cancel out b/c its in equilibrium, so you just have the tension force going upward and mg going down so mg - T = 0, mg = T.

 

[kyle8921]

Thank you for reaching out for help with this problem. It seems like you have a good understanding of the basic principles involved in this pulley system. However, your initial answer of 215.6N is not quite correct. Let's take a closer look at the forces involved in this system.

First, let's define our variables:

m = mass of the crate (44 kg)
g = acceleration due to gravity (9.8 m/s^2)
T1 = tension in the chain connecting the upper pulley to the ceiling
T2 = tension in the chain connecting the lower pulley to the crate

Now, let's break down the forces acting on the crate. We have the weight of the crate (mg) pulling down, and we have the tension in the two chains pulling up. Since the crate is being lifted at a constant speed, we know that the net force on the crate is zero (Newton's First Law). This means that the upward forces must balance out the downward force. Therefore, we can set up the following equation:

T1 + T2 = mg

We also know that the tension in the two chains must be equal, since they are connected to the same crate. So we can rewrite the equation as:

2T = mg

Now, we can solve for T by plugging in our values:

2T = (44 kg)(9.8 m/s^2)
T = 215.6N

So, the tension in each chain is actually 215.6N, which is the same as your initial answer. However, it is important to note that this is the tension in each chain, not the total tension. The total tension in the system would be 2T, or 431.2N.

I hope this helps clarify the concept for you. If you have any further questions or concerns, please don't hesitate to reach out. Good luck with your resubmission!