Studies of gymnasts show that their high rate of injuries to the Achilles tendon is due to tensions in the tendon that typically reach 12 times body weight. That force is provided by a pair of muscles, each exerting a force at 23 ∘ to the vertical, with their horizontal components opposite.

For a 53-kg gymnast, find the force in each of these muscles.

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

Question

memilydem memilydem

26-09-2016
Physics

Answered

Studies of gymnasts show that their high rate of injuries to the Achilles tendon is due to tensions in the tendon that typically reach 12 times body weight. That force is provided by a pair of muscles, each exerting a force at 23 ∘ to the vertical, with their horizontal components opposite.

For a 53-kg gymnast, find the force in each of these muscles.

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

Verified Answer :

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scme1702 scme1702 · Answer 1 · 2016-10-07T15:07:39-04:00

The horizontal components, being opposite in direction, will produce a shearing effect on the tendon, leading to injury. Thus, they will be added.
As the angle of 23 is from the vertical, we calculate the horizontal component by using
Weight acting sin(23)
And multiply it by 2 to get the total shearing force
The weight acting is 12 times their body weight. Thus:
53 9.81 12 = 6239.2 Newtons
The total force acting on the tendon:
2 sin(23) * 6239.2
= 4,880
= 4,900 Newtons (2 significant figures)