Determining reaction forces and angle

[brostingy]

Homework Statement

An assembly is shown in Figure 1, GH, HK and HNL are three cables. The mass of box L is 350 kg,
a) Determine the mass of box K in order to make angle teta = 30 degrees
b) Determine the reaction forces at supports G and N.


i started by converting the 350kg to a force using F=ma, but stuck there...

help

digram attached to post

 

[droc22]

First, do FBD of the pulley that K is on.

$$\Sigma$$F_y=0=m_Lgsin30-m_kg

That solves m_k.

Reaction at G is x-component of the above FBD Gx = m_Lgcos30.

I'm sure you can figure out Rn now.

Hope that helps.

 

[brostingy]

ye thanks, i think i follow you, but just to clarify,

FDB is:

mass of L x gravity x sin30 - mass of K x gravity = 0

reaction at G:

G = mass of L x gravity x cos30

Rn:

should be:

y + x values...

sorry to sound dumb... :(

 

[droc22]

I won't give you the answers, but I'll give you the steps.

1. Draw FBD of Pulley K
2. Solve for x and y components to find mass of k and Rg. HINT: the magnitude (or hypotenuse) of the rope that's on 30 deg is the transferred weight of L
3. Draw FBD of Pulley L. You need a reaction force going up for Rn, and two forces (one on an angle of 30 deg-Also, remember 3rd Law) caused by the weight of Box L.
4. Split this diagram into x and y components and solve for Rnx and Rny, because the rest is know.

Do that make sense? Let me know what you get.