Solving Tension in Massless, Frictionless Pulley System

[jdroidxw]

Homework Statement

What is the tension T? The pulley is massless and frictionless.
m1=661 g, w2=5 N, g=9.8 m/s²
Picture attached

Homework Equations

T=w1+w2 ??

The Attempt at a Solution

First of all, I converted 661 g into kg. Next I multiplied that by g. I added that value to the 5N and I thought that was the T which was wrong.

 

[Spinnor]

If you draw a free-body diagram you don't have to think as hard IMO. See the attached.

 

[jdroidxw]

Where did you get the 2T' from?

 

[Spinnor]

I drew a free-body diagram for both masses. The tension T will not be the same as the tension in the other rope. Do the two free-body diagrams I drew make sense?

 

[rwisz]

I would approach this problem by first understanding the properties of a massless, frictionless pulley system. In this type of system, the pulley itself does not have any mass and there is no friction present, meaning that the tension on either side of the pulley must be equal.

To find the tension in this system, we can use the equation T = m1g + m2g, where m1 and m2 are the masses on either side of the pulley and g is the acceleration due to gravity. In this case, m1 is given as 661 g, which is equal to 0.661 kg, and m2 is given as w2, which is equal to 5 N. Therefore, the tension T is equal to (0.661 kg)(9.8 m/s2) + 5 N = 11.5 N.

It is important to note that in a massless, frictionless pulley system, the tension remains constant throughout the system. This means that the tension T is the same on both sides of the pulley and does not change as the system moves. The equation T = m1g + m2g can be used to find the tension at any point in the system, as long as the masses and acceleration due to gravity remain constant.

In conclusion, the tension T in this massless, frictionless pulley system is equal to 11.5 N.