An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough such that any person inside is held up against the wall when the floor drops away (Fig. P6.65). The coefficient of static friction between person and wall is μs, and the radius of the cylinder is R. (a) Show that the maximum period of revolution necessary to keep the person from falling is T = (4π2Rμs/g)½ (b) Obtain a numerical value for T if R = 4.00 m and μs = 0.400. How many revolutions per minute does the cylinder make?

An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough such that any person inside is held up against the wall when the floor drops away (Fig. P6.65). The coefficient of static friction between person and wall is μs, and the radius of the cylinder is R. (a) Show that the maximum period of revolution necessary to keep the person from falling is T = (4π2Rμs/g)½ (b) Obtain a numerical value for T if R = 4.00 m and μs = 0.400. How many revolutions per minute does the cylinder make?

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

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 6OQ: Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon...

See similar textbooks

Similar questions

Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
Instead of moving back and forth, a conical pendulum moves in a circle at constant speed as its string traces out a cone (Fig. P6.68). One such pendulum is constructed with a string of length L = 12.0cm and bob of mass 0.210 kg. The string makes an angle = 7.00 with the vertical, a. What is the radial acceleration of the bob? b. What are the horizontal and vertical components of the tension force exerted by the string on the bob?
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
Since March 2006, NASAs Mars Reconnaissance Orbiter (MRO) has been in a circular orbit at an altitude of 316 km around Mars (Fig. P6.81). The acceleration due to gravity on the surface of the planet Mars is 0.376g, and its radius is 3.40 103 km. Assume the acceleration due to gravity at the satellite is the same as on the planets surface. a. What is MROs orbital speed? B. What is the period of the spacecrafts orbit? FIGURE P6.81
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 8.8 m and the coefficient of friction between the rider and the wall is 0.653, 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 rocket is fired straight up, and it burns out at an altitude of 250 km when traveling at 6.00 km/s (at this point the rocket is too far from the surface of the earth to be affected by the earth gravitational pull). What maximum distance from the earth surface does the rocket travel before falling back to the earth? The radius of the earth is RE = 6.37 x 106 meters, the mass of the earth is ME = 5.98 x 1024 kg and G = 6.67 x 10-11 N∙m2/kg2
A box descends a ramp and lands on a surface. The box exits the side of the table as it meets the bottom of the tamp, becoming a horizontal projectile. It lands x metres away from the table. The same ramp may be rolled down by a solid sphere with the same coefficient of friction, mass, and height. Will the sphere land a long way away? fewer than a lot more At a similar size B. Have a paragraph-length description of the logic.
You are working during your summer break as an amusement park ride operator. The ride you are controlling consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (Fig. P6.7). The coefficient of static friction between a person of mass mand the wall is us, and the radius of the cylinder is R. You are rotating the ride with an angular speed w suggested by your supervisor. (a) Suppose a very heavy person enters the ride. Do you need to increase the angular speed so that this person will not slide down the wall? (b) Suppose someone enters the ride wearing a very slippery satin workout outfit. In this case, do you need to increase the angular speed so that this person will not slide down the wall?
A distant planet has a mass of 5.00 x 1023 kg and a radius of 6.00 x 106 m. Someone is standing on the surface of the planet and throws a rock straight up with initial speed of 7.0 m/s. What is the maximum hight reached by the rock above the point from where it was thrown?
An asteroid, whose mass is 2.0 × 10-4 times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 2.7 times the Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth? (a) Number i Units (b) Number i Units
A rocket with mass 5.00×103 kgkg is in a circular orbit of radius 7.50×106 mm around the earth. The rocket's engines fire for a period of time to increase that radius to 8.60×106 mm, with the orbit again circular. What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? Express your answer with the appropriate units. Enter positive value if the kinetic energy increases and negative value if the kinetic energy decreases. What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? Express your answer with the appropriate units. Enter positive value if the gravitational potential energy increases and negative value if the gravitational potential energy decreases. How much work is done by the rocket engines in changing the orbital radius? Express your answer with the appropriate units.
Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.