A mother pushes her child on a swing so that his speed is 9.1 m/s at the lowest point of his path. The swing is attached to a point 2.1 m above the child's center of mass when the swing is motionless. (A) What is the centripetal acceleration of the child at the low point in m/s²? (B) What is the magnitude of the forest that the child exerts on the seat at the lowest point if his mass is 18.5 kg in N?

A mother pushes her child on a swing so that his speed is 9.1 m/s at the lowest point of his path. The swing is attached to a point 2.1 m above the child's center of mass when the swing is motionless. (A) What is the centripetal acceleration of the child at the low point in m/s²? (B) What is the magnitude of the forest that the child exerts on the seat at the lowest point if his mass is 18.5 kg in N?

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Description: A mother pushes her child on a swing so that his speed is 9.1 m/s at the lowest point of his path. The swing is attached to a point 2.1 m above the child's center of mass when the swing is motionless.(A) What is the centripetal acceleration of the ch

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

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 6OQ: A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with...

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A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure OQ5.6. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) Of these points, is there a point where the bob has nonzero radial acceleration and zero tangential acceleration? If so, which point? What is the direction of its total acceleration at this point? (b) Of these points, is there a point where the bob has nonzero tangential acceleration and zero radial acceleration? If so, which point? What is the direction of its total acceleration at this point? (c) Is there a point where the bob has no acceleration? If so, which point? (d) Is there a point where the bob has both nonzero tangential and radial acceleration? If so, which point? What is the direction of its total acceleration at this point? Figure OQ5.6
Suppose you are a roller coaster ride designer and you begin a new design with safety in mind. Safety regulations state that the riders' centripetal acceleration should be no more than n = 1.65g at the top of the hump and no more than N = 5.50g at the bottom of the hoop. Previous sections of the ride give the train a speed of 11.3 m/s at the top of the incline, which is h = 37.5 m above the ground (see figure). Ignoring the effects of friction and air resistance: (a) What is the minimum radius Rhump you can use for the semi-circular hump? (b) What is the minimum radius Rloop you can use for the vertical loop? h R hump R loop
See Conceptual Example 6 to review the concepts involved in this problem. A 10.5-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 90.8 cm is between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 3.88 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm.
See Conceptual Example 6 to review the concepts involved in this problem. A 9.49-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 92.1 cm is between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 1.78 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm. Units (a) Number Units (b) Number
A 2.00Kg puck on a frictionless horizontal surface on the Earth is constrained to a circular orbit by a 4.00 meter long string attached to a vertical rod. Assume the string is attached to the rod by a ring that lets it revolve around the rod without friction. The string can withstand up to a 50.0N tension without breaking. Once the puck is released, it slides on a horizontal dirt surface with a coefficient of kinetic friction of 0.15. How far will it go to where it stops and how much time does it take to stop?
A roller-coaster car has a mass of 1220 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18.1 m, its speed is not changing. (a) At the top of the hill, what is the normal force (using the negative sign for the downward direction) FN on the car from the track if the car's speed is v- 9.49 m/s? (b) What is F if v- 16.7 m/s? (a) Number i (b) Number i Units Units
See Conceptual Example 6 to review the concepts involved in this problem. A 10.8-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 61.6 cm is between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 1.99 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm. (a) Number (b) Number Units Units #
A kid whirls a rock of mass 0.5 kg in a vertical circle of radius 0.80 m. (a) What is the minimum speed of the rock at the top of the circle such that the rope does not go slack? (b) What is the speed of the rock at the bottom of the circle if the tension in the rope is 17.0 N?
Caroline takes her baby sister Hannah to the neighborhood park and places her in the seatof the children’s swing. Caroline pulls the L = 1.8 m long chain back to make an angle θ = 26◦ withrespect to the vertical and lets 14 kg Hannah (swing mass included) go. (a) Determine Hannah’s speed at the lowest point in the trajectory. (b) What is the tension in the swing chain at this low point? Assume the chain itself has negligible mass.
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At amusement parks, there is a popular ride where the floor of a rotating cylindrical room falls away, leaving the backs of the riders “plastered” against the wall. Suppose the radius of the room is 3.122 m and the coefficient of friction between the rider and the wall is 0.47, what is the minimum the safe speed of the wall for the rider not to drop when the floor falls away. Use g=9.8 m/s2.
A disk of mass m = 0.140 kg is attached to a lightweight, taut string which keeps it in circular motion, as shown in the figure below. The disk slides on a horizontal table with negligible friction at speed v, = 80.0 cm/s, and the radius of its circular path is r, = 36.0 cm. The string passes a small hole in the table and is initially held in place. The string is then slowly pulled downward a distance of 12.0 cm. How much work (in J) is done on the disk? Need Help? Read It