Chapter 8, Problem 24P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P8.24a. The total gravitational force on the body, F → g , is supported by the force n → exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P8.24b, where T → is the force exerted by the Achilles tendon on the foot and R → is the force exerted by the tibia on the foot. Find the values of T, R, and θ when Fg = n = 700. N.Figure P8.24

To determine
The values of T, R and θ .

Explanation

Given Info: The total gravitational force on the body is Fg , force exerted by the floor on the toes is n, force exerted by the Achilles tendon on the foot is T and force exerted by the tibia on the foot is R.

Explanation:

The following free body diagram shows the force acts on the foot.

From the free body diagram, employing equilibrium condition at the point O (pivot point) in the horizontal position is,

âˆ‘Fx=0

• âˆ‘Fx is the net force acting on the foot

Write the formula to calculate âˆ‘Fx .

âˆ‘Fx=Rsin15Î¿âˆ’TsinÎ¸

Rewrite the equilibrium condition by substituting the above relation for âˆ‘Fx .

Rsin15Î¿âˆ’TsinÎ¸=0

The above relation gives the following result.

Rsin15Î¿=TsinÎ¸ (1)

• Fx is the force acts in the horizontal direction.
• R is the force exerted by the tibia on the foot.
• T is the force exerted by the Achilles tendon on the foot.

Rewrite the above relation in terms of R.

R=TsinÎ¸sin15Â° (2)

From the free body diagram, employing equilibrium condition at the point O (pivot point) in the vertical position is,

âˆ‘Fy=0700â€‰Nâˆ’Rcos15Â°+TcosÎ¸=0

Rewrite the above relation.

(700â€‰N)+TcosÎ¸=Rcos15Î¿ (3)

At the point O, the net torque is zero. Therefore,

âˆ‘Ï„O=0âˆ’(700â€‰N)(18.0â€‰cm)cosÎ¸+T(25.0â€‰cmâˆ’18.0â€‰cm)=0 . (4)

From the above equations,

(1+tan215Î¿)cos4Î¸+[(2tan15Î¿)(0

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