A muscle builder holds the end of a massless rope. At the center of the rope, a 15-kg ball is hung. What is the tension in the rope if the angle of depression between the end of the rope to where...

A muscle builder holds the end of a massless rope. At the center of the rope, a 15-kg ball is hung. What is the tension in the rope if the angle of depression between the end of the rope to where the ball is hung is 4,5 degrees? Please explain your answer.

Thank you. 

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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

As the ball is hung from the centre of the rope, tensions in either side of the rope will be equal. So would be the case for angles of depression on either side. The situation is depicted in the attached figure.

Balancing of forces,

In the X-direction:

`-Tcos4.5^o +Tcos4.5^o=0`

In the Y-direction:

`Tsin4.5^o +Tsin4.5^o-m*g=0`

`2Tsin4.5^o=15*9.81`

`rArr T=(15*9.81)/(2sin4.5^o)`

`=937.75 N`

Therefore, tension in the rope is 937.75 N.

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