PHYSICS HELP! (Will award best answer!)?

Part a)

The forces acting on the boom are its own weight (Mg) originating from the center of mass

at half its length. The weight (mg) also acts on it together with the tension and also the

hinge has a counterforce. These can all be separated into components and unfortunately

I have no possibility to provide a picture.

Part b)

Torque: τ = rF

We can choose the hinge as the reference and balance torques about that point.

Sum of all torques is zero since the boom is held in equilibrium:

Let clockwise be the positive direction of torque, ∑τ+ = 0 =>

(½L)Mgcos50° + (L)mgcos50° – (¾L)Tsin70° = 0

The boom's length L can be crossed on both sides and won't be needed anymore.

So this rearranges to:

gcos50°(½M+m) = ¾Tsin70°

T = 4gcos50°(½M+m) / 3sin70°

Acceleration of gravity g=9.8m/s² and you also have M=65kg and m=150kg. Plug in and calculate:

T = 1631 N

(≈ 1.6 kN to two significant figures)

Part c)

The force of the hinge countering the forces from the cable, mass and boom whose components

are directed along the boom.

Fhinge = gsin50°(M+m) + Tcos70°

Fhinge = 2172 N

or 2.2 kN to two significant figures, directed at 50degrees, upwards along the boom

To determine the tension in the cable, let’s do a torque problem. Let the pivot point be at the hinge. The tension in the cable produces counter clockwise torque. The weights of the box and the boom produce clockwise torque.

¾ * 7 = 5.25 meter

Counter clockwise torque = T * 5.25 * sin 70

Clockwise torque = 150 * 9.8 * 7 *cos 50 = 10,290 * cos 50

Clockwise torque = 65 * 9.8 * 3.5 * cos 50 = 2,229.5 * cos 50

Total clockwise torque = 12,519.5 * cos 50

T * 5.25 * sin 70 = 12,519.5 * cos 50

T = 12,519.5 * cos 50 ÷ (5.25 * sin 70) = 2384⅔ * cos 50 ÷ sin 70

This is approximately 1631 N.

cos 50° = 0.643

((65*7/2+150*7)*cos 50°)*g = (Ty*7*3/4*cos 50)

Ty = (65*7/2+150*7)*g*4/21 = 243.33 g N

T = Ty/(sen (180-(90+70)) = 243.33/0.342*g = 711.5*g N (≈ 6977 N)

Fy = m*g = (150+65)*g N

Fx = T*cos 20°= 6977*0.94 = 6558 N