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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 ride’s structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of θ = 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
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Chapter 6 Solutions
Physics for Scientists and Engineers
- A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown in Figure P6.48. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead slay motionless relative to the turning circle? (b) What If? Repeat the problem, this time taking the period of the circles rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem. Figure P6.48arrow_forwardA small block with mass 0.0500 kg slides in a vertical circle of radius 0.475 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 3.80 N . In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.665 N . How much work was done on the block by friction during the motion of the block from point A to point B?arrow_forwardA small block with mass 0.0300 kgkg slides in a vertical circle of radius 0.425 mm on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point AA, the magnitude of the normal force exerted on the block by the track has magnitude 3.90 NN . In this same revolution, when the block reaches the top of its path, point BB, the magnitude of the normal force exerted on the block has magnitude 0.675 NN . 1)How much work was done on the block by friction during the motion of the block from point AA to point BB?arrow_forward
- Peter propels a penguin with mass 10.0kg from 2.50m above the ground at an angle 30.0o from the horizontal axis (ground), with an initial speed of 15.0 m/s. Assuming the penguin remains rigid (scared, so assume the particle model!) and ignoring any rotational effects, What is the horizontal range of the penguin (where it lands on the ground)? a. 23.6 meters b. 24.1 meters c. 47.1 meters d. 19.9 meters e. 31.5 metersarrow_forwardOne model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?arrow_forwardA 50.0-kg child stands at the rim of a merry-go-round of radius 2.95 m, rotating with an angular speed of 4.00 rad/s. (a) What is the child's centripetal acceleration? (b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round? Yes/Noarrow_forward
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