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An amusement park ride 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. P5.60). 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
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Chapter 5 Solutions
Principles of Physics: A Calculus-Based Text
- The mass of a roller-coaster car, including its passengers, is 500 kg. Its speed at the bottom of the track in Figure P6.16 is 19 m/s. The radius of this section of the track is r1 = 25 m. Find the force that a seat in the roller-coaster car exerts on a 50-kg passenger at the lowest point.arrow_forwardInstead 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?arrow_forwardJack sits in the chair of a Ferris wheel that is rotating at a constant 0.100 rev>s. As Jack passes through the highest point of his circular path, the upward force that the chair exerts on him is equal to one-fourth of his weight. What is the radius of the circle in which Jack travels? Treat him as a point mass.arrow_forward
- A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?arrow_forwardA 3.0-kg rocket-propelled toy car has a speed of 6.0 m/s as it rides inverted at the top of a vertical circular track of radius 1.5 m. What is the force (in Newtons) exerted by the track on the car?arrow_forwardA jet airplane is in level flight. The mass of the airplane is m 8970 kg. The airplane travels at a constant speed around a 9.77 mi and makes one revolution every T 0.129 h. Given that the lift force acts circular path of radius R perpendicularly upward from the plane defined by the wings, what is the magnitude of the lift force acting on the airplane? R L kN At what angle is the airplane banked? x10arrow_forward
- A string 0.5 m long is used to whirl a 0.5 kg stone in a vertical circle at a uniform velocity of 5m/s. What is the tension in the string (a) when the stone is at the top of the circle and (b) when the stone is at the bottom of the circle?arrow_forwardIn a recent study of how mice negotiate turns, the mice ran BIO around a circular 90° turn on a track with a radius of 0.15 m. The maximum speed measured for a mouse (mass = 18.5 g) running around this turn was 1.29 m/s. What is the minimum coefficient of friction between the track and the mouse's feet that would allow a turn at this speed?arrow_forwardIn an old-fashioned amusement park ride, passengers stand inside a 4.6-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed." What is the minimum angular speed, in rpmrpm, for which the ride is safe?arrow_forward
- While driving along a country lane with a constant speed of 17 m/s, you encounter a dip in the road. The dip can be approximated as a circular arc with a radius of 65m. What is the normal force exerted by the car seat on an 80kg passenger when the car is at the bottom of the dip?arrow_forwardA Wall of Death is a carnival show featuring a motorcyclist rides along the vertical wall of the cylinder and performs various stunts while doing so. Given that the radius of the cylinder is 7 m and the static coefficient of friction is 0.8, what is the minimum speed in m/s2 that the motorcyclist must do to prevent the motorcycle to slip from the wall?arrow_forwardIn the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle = 25.6°. The slab has length L = 43.4 m, thickness T = 6.23 m, and width W = 13.6 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.351. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.42 cm² and will snap under a shearing stress of 3.57 × 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.arrow_forward
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