Mass of M2 in kg: Solve Mass/Tension Problem

[missyjane]

A left-hand cable has a tension T1 and makes an angle of 49 with the horizontal. The right-hand cable has a tension T3 and makes an angle of 51 with the horizontal. A weight M1 is on the left and a weight M2 is on the right. A cable connecting the two weights has a tension 32N and is horizontal. The acceleration due to gravity is 9.8 m/s^2. What is the mass of M2 in kg?

I have no clue where to even start. Help please!

 

[Päällikkö]

Well, as the system isn't accelerating, the resultant of forces must equal 0.

 

[missyjane]

I'm still lost

 

[Pyrrhus]

Draw a freebody diagram for each body, and then do a sum of forces. Remember to consider the weight of the bodies.

 

[missyjane]

That's what I'm trying to find though...the mass of the second weight.

 

[missyjane]

Ok, I know I have to find T1 using the given angle and that T2=32N...but how does that information help me?

 

[Dorothy Weglend]

Ok, I know I have to find T1 using the given angle and that T2=32N...but how does that information help me?

If I am visualizing this correctly, the tension T1 has components to the left and up. These are balanced by T2 to the right, and the weight of the mass (m1 * g) downward. Nothing is accelerating, so the sum of all these forces is zero.

I will give you the horizontal equation, to get you started. The horizontal component of T1 is T1 cos 49. So you have T2 - T1 cos 49 = 0. If you solve this, you will have the value of T1. You can then use this in the vertical forces to get the value of the mass.

You proceed the same way on the right side, to get the tension T3 and the mass M2.