You decide to hang a plant from a 1.5-m-long 2.0-kghorizontal beam that is attac

Question

You decide to hang a plant from a 1.5-m-long 2.0-kghorizontal beam that is attached by a hinge to the wall on the left. A cable attached to the right end goes 37above the beam to a connecting point above the hinge on the wall. You hang a 12-kg pot from the beam 1.4 maway from the wall. (Figure 1)

Part A

Determine the force that the cable exerts on the beam.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the force that the wall hinge exerts on the beam (its x- and y-components).

Express your answers using two significant figures separated by a comma.

Part C

Determine the magnitude of the force that the wall hinge exerts on the beam.

Express your answer to two significant figures and include the appropriate units

Part D

Determine the direction of the force that the wall hinge exerts on the beam (counted from the positive x-axis).

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

here,

mass of beam , mb = 2 kg

length , l = 1.5 m

theta = 37 degree

mass of pot , m = 12 kg

x = 1.4 m

A)

let the force exerted by the cable be t

taking moment of force about the hinge

x*m*g + (l/2)*mb*g - t * sin(theta) * l = 0

1.4 * 12*9.8 + 0.75 * 2*9.8 - t * sin(37)*1.5 = 0

t = 198.67 N

the force exerted by the cable is 198.67 N

B)

let the force exerted by the wall on the beam be Fx and Fy

Fx - t * cos(theta) = 0

Fx = 198.67 * cos(37)

Fx = 158.66 N

and equating the forces vertically

Fy = 12 * 9.8 + 2 * 9.8 - t * sin(theta)

Fy = 17.64 N

C)

F = sqrt(Fx^2 + Fy^2)

F = 159.6 N

the magnitude of the force that the wall hinge exerts on the beam is 159.6 N

D)

theta = arctan(17.64/159.6)

theta = 6.31 degree

the direction of the force that the wall hinge exerts on the beam is 6.31 degree

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