Answer:
Part a)
![T_L = 155.4 N](https://tex.z-dn.net/?f=T_L%20%3D%20155.4%20N)
Part b)
![T_R = 379 N](https://tex.z-dn.net/?f=T_R%20%3D%20379%20N)
Explanation:
As we know that mountain climber is at rest so net force on it must be zero
So we will have force balance in X direction
![T_L cos65 = T_R cos80](https://tex.z-dn.net/?f=T_L%20cos65%20%3D%20T_R%20cos80)
![T_L = 0.41 T_R](https://tex.z-dn.net/?f=T_L%20%3D%200.41%20T_R)
now we will have force balance in Y direction
![mg = T_L sin65 + T_Rsin80](https://tex.z-dn.net/?f=mg%20%3D%20T_L%20sin65%20%2B%20T_Rsin80)
![514 = 0.906T_L + 0.985T_R](https://tex.z-dn.net/?f=514%20%3D%200.906T_L%20%2B%200.985T_R)
Part a)
so from above equations we have
![514 = 0.906T_L + 0.985(\frac{T_L}{0.41})](https://tex.z-dn.net/?f=514%20%3D%200.906T_L%20%2B%200.985%28%5Cfrac%7BT_L%7D%7B0.41%7D%29)
![514 = 3.3 T_L](https://tex.z-dn.net/?f=514%20%3D%203.3%20T_L)
![T_L = 155.4 N](https://tex.z-dn.net/?f=T_L%20%3D%20155.4%20N)
Part b)
Now for tension in right string we will have
![T_R = \frac{T_L}{0.41}](https://tex.z-dn.net/?f=T_R%20%3D%20%5Cfrac%7BT_L%7D%7B0.41%7D)
![T_R = 379 N](https://tex.z-dn.net/?f=T_R%20%3D%20379%20N)
The state of matter would have to be solid
Answer:
60 boxes
Explanation:
The work done by lifting a single box is equal to the force applied (the weight of the box) times the displacement of the box:
![W_1 = Fd=(12.0 N)(5.00 m)=60 J](https://tex.z-dn.net/?f=W_1%20%3D%20Fd%3D%2812.0%20N%29%285.00%20m%29%3D60%20J)
Power is related to the work done by the equation:
![P=\frac{W}{t}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BW%7D%7Bt%7D)
where W is the work done and t is the time. In this problem, we are told that the power used is P=60.0 W, while the time taken is t = 1 min = 60 s, so the total work done must be
![W=Pt=(60.0 W)(60 s)=3600 J](https://tex.z-dn.net/?f=W%3DPt%3D%2860.0%20W%29%2860%20s%29%3D3600%20J)
Therefore, the number of boxes that she has to lift in order to use this power is the total work divided by the work done in lifting each box:
![N=\frac{W}{W_1}=\frac{3,600 J}{60 J}=60](https://tex.z-dn.net/?f=N%3D%5Cfrac%7BW%7D%7BW_1%7D%3D%5Cfrac%7B3%2C600%20J%7D%7B60%20J%7D%3D60)
Assuming you're working in a 3D cartesian coordinate system, i.e. each point in space has an x, y, and z coordinate, you add up the forces' x/y/z components to find the resultant force.