A $\backslash (710-\backslash$mathrm$\{$N$\}\backslash )$ athlete standing on one foot on a very smooth gym floor litts his body by pivoting his foot upward through a $\backslash (30^\{\backslash$circ$\}\backslash )$ angle, balancing all of his weight on the ball of the foot. The forces on the foot bones from the rest of his body are due to the Achilles tendon and the ankle joint. $($See the figure below $($Figure $1).)$ The Achilles tendon acts perpendicular to a line through the heel and toes; it is this line that has rotated upward through $\backslash (30^\{\backslash$circ$\}\backslash ).$ Assume that the weight of the foot is negligible compared with that of the rest of the body.

Part A

What is the magnitude of the force that the floor exerts on the athlete's foot? Express your answer in newtons.

$[$

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Part B

What is the direction of the force that the floor exerts on the athlete's foot?

upward

downward

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Part C

What is the tension in the Achilles tendon?

Express your answer in newtons.

T

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Part D

Find the horizontal component of the force that the ankle joint exerts on the foot.

Express your answer in newtons.

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Part E

Find the vertical component of the force that the ankle joint exerts on the foot.

Express your answer in newtons.

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Part F

Use these components to find the magnitude of this force. Express your answer in newtons.

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