Question 1: An object with a mass of m = 144 kg is suspended by a rope from the

Question

Question 1:

An object with a mass of m = 144 kg is suspended by a rope from the end of a uniform boom with a mass of M = 74.5 kg and a length of l = 9.82 m. The end of the boom is supported by another rope which is horizontal and attached to the wall as shown in the figure.

A.)The boom makes an angle of ? = 63.8° with the vertical wall. Calculate the tension in the vertical rope.

B.)Calculate the tension in the horizontal rope. (The horizontal and the vertical ropes are not connected to each other. They are both independently attached to the end of the boom.)

Question 2:

A.) An object performing simple harmonic oscillation covers a distance of 125 cm in one complete period of 3.20 s. Determine the maximum speed of the object.

(122.6 m/s is wrong)

B.)Determine the maximum acceleration of the object.

(240.7 cm/s^2 is wrong)

Explanation / Answer

a) Tension in vertica rope = mg = 144x9.81 =1412.64 N

b) balancing moment about wall point,

L/2 x Mgsin63.8   + L x mgsin63.8 - L x Tcos63.8 = 0

(9.82 x 74.5 x 9.81 sin63.8 /2) + (9.82 x144 x 9.81 sin63.8) = 9.82 T cos63.8

T = 3613.50 N

-----------------------------------------

amplitude = 125/4 = 31.25 cm

w = 2pi / T = 2pi / 3.20 = 1.96 rad/s

a) Vmax = Aw = 0.3125 x 1.96 = 0.614 m/s

b) a_max= Aw^2 = 0.3125 x 1.96^2 = 1.20 m/s^2

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