### Understanding Forces in a Strenuous PositionWhen a person stands on tiptoe (a strenuous position), the position of the foot is illustrated in Figure a. The total gravitational force on the body, \( \vec{F_g} \), is supported by the force \( \vec{n} \) exerted by the floor on the toes of one foot. A mechanical model of the situation is depicted in Figure b, where:- \( \vec{T} \) is the force exerted by the Achilles tendon on the foot- \( \vec{R} \) is the force exerted by the tibia on the footYour task is to find the values of \( T \), \( R \), and \( \theta \) given that \( F_g = n = 770 \, \text{N} \). For \( \theta \), choose the smaller angle between 0° and 90°.#### Diagram Explanation:- **Figure a** shows an anatomical representation of the foot with the tibia and Achilles tendon labeled. - **Figure b** presents a simplified diagram with forces: - \( \vec{n} \) acts vertically upwards from the ground. - \( \vec{T} \) is oriented downwards at an angle \( \theta \). - \( \vec{R} \) is at an angle of \( 15.0^\circ \) to the vertical. - Dimensions are marked as 18.0 cm and 25.0 cm, indicating lever arms for the forces.#### Calculate the forces:- \( T = \) [input field] N- \( R = \) [input field] N- \( \theta = \) [input field] °Ensure correct trigonometric and mechanical principles are applied to solve the forces and angle.**Submit Answer** [Button]

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 69P

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BIO The arm in Figure P10.35 weighs 41.5 N. The gravitational force on the arm acts through point A. Determine the magnitudes of the tension force F1 in the deltoid muscle and the force Fs exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. Figure P10.35
An object is being weighed using an unequal-arm balance (Fig. P14.76). When the object is in the left pan, a downward force of 3.0 N must be exerted on the right pan to balance the gravitational force on the object. When the object is in the right pan, a downward force of 2.0 N must be exerted on the left pan to balance the gravitational force on the object. Determine the magnitude of the gravitational force on the object. FIGURE P14.76
A makeshift sign hangs by a wire that is extended over an ideal pulley and is wrapped around a large potted plant on the roof as shown in Figure P6.10. When first set up by the shopkeeper on a sunny and dry day, the sign and the pot are in equilibrium. Is it possible that the sign falls to the ground during a rainstorm while still remaining connected to the pot? What would have to be true for that to be possible? FIGURE P6.10 Problems 10 and 11.
BIO When a gymnast performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P10.85a. In this maneuver, the gymnasts feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (lats) and the pectoralis major (pecs). One of the rings exerts an upward fore Fh on a hand as shown in Figure P10.85b. The force Fs is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force Fm on the arm. (a) Using the information in the figure, find the magnitude of the force Fm. (b) Suppose an athlete in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45 angle with the horizontal rather than being horizontal. Why is this position easier for the athlete? Figure P10.85
A Frisbee flies across a field. Determine if the system has translational kinetic energy, rotational kinetic energy, neither, or both as determined by the observer in each of the following cases. a. The observer watches the flight of the Frisbee across the field from a park bench. b. The observer is a dog that runs directly beneath the Frisbee. c. The observer is an ant at rest on the Frisbee.
Why is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he slips out of his seat and climbs to the top of the rides structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of = 20.0 with the horizontal as shown in Figure P6.32. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5.32 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is 0.700. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the sitting, pouting boy rotates in a circular path at a speed of 3.75 m/s. Figure P6.32
Unreasonable Results A mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path. The swing is suspended 2.00 m above the child's center of mass. (a) What is the magnitude of the centripetal acceleration of the child at the low point? (b) What is the magnitude of the force the child exerts on the seat if his mass is 18.0 kg? (c) What is unreasonable about these results? (d) Which premises are unreasonable or inconsistent?
A One end of a metal rod of weight Fg and length L presses against a corner between a wall and the floor (Fig. P14.64). A rope is attached to the other end of the rod. Find the magnitude of the tension in the rope if the angle between the rod and the rope is 90.
A certain orthodontist uses a wire brace to align a patients crooked tooth as in Figure P5.4. The tension in the wire is adjusted to have a magnitude of 18.0 N. Find the magnitude of the net force exerted by the wire on the crooked tooth.
To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam around the house(Fig. P13.66). When a hamsteris in such a ball, it can cross atypical room in a few minutes.Estimate the total kinetic energyin the ball-hamster system. FIGURE P13.66 Problems 66 and 67
A uniform pole is propped between the floor and the ceiling of a room. The height of the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling is 0.576. The coefficient of static friction between the pole and the floor is greater than that between the pole and the ceiling. What is the length of the longest pole that can be propped between the floor and the ceiling?
(a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 20.0 with the horizontal. A piece of luggage having mass 30.0 kg is placed on the carousel at a position 7.46 m measured horizontally from the axis of rotation. The travel bag goes around once in 38.0 s. Calculate the force of staticfriction exerted by the carousel on the bag. (b) The drive motor is shifted to turn the carousel at a higher constant rate of rotation, and the piece of luggage is bumped to another position, 7.94 m from the axis of rotation. Now going around once in every 34.0 s, the bag is on the verge of slipping down the sloped surface. Calculate the coefficient of static friction between the bag and the carousel.

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