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

Physics

Will Waters

7 December, 01:40

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.

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Answers (1)

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Lyric · Answer 1

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)