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weqwewe [10]
3 years ago
15

To carry a 100 pound cylindrical weight, two people lift on the ends of short ropes that are tied to eyelet on the top center of

the cylinder. Each rope makes an angle of theta degrees with the vertical. Write the tension T of each rope as a function of Theta.
Mathematics
2 answers:
blagie [28]3 years ago
8 0

Answer:

\boxed {\displaystyle T=\frac{m.g}{2cos\theta}}

Step-by-step explanation:

<u>Net Force</u>

The net force exerted on an object is the sum of all vector forces applied to it. If no acceleration is achieved, the net force is zero.

We have three forces applied to the cylindrical weight: Its own weight and the two components of the tension of each rope. Knowing they form an angle \theta with the vertical, then each component is given by

T_y=Tcos\theta

The sum of all forces in the vertical direction is

F_y=2T_y-m.g

The object is not accelerated, thus

2T_y-m.g=0

2Tcos\theta=m.g

Solving for T

\boxed {\displaystyle T=\frac{m.g}{2cos\theta}}

Ostrovityanka [42]3 years ago
6 0

Answer:

T=mg/2cos \theta

Step-by-step explanation:

#Given that each rope is tied to the cylinder top and makes the same \angle \theta with the vertical,:

Let tension on the rope be T

#The vertical component of each T is, Tcos \theta

Total vertical component is 2Tcos \theta

We know that

F=ma\\F=2Tcos \theta\\ma=mg\\\\\therefore T=mg/2cos \theta    #where g is gravitational acceleration.

Hence the tension of each rope is T=mg/2cos \theta

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