BackThe Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of m. Its name comes from its arms, each of which can function as a second hand (so that it makes one revolution every s). A passenger weighs N at the weight-guessing booth on the ground. What is his apparent weight at the highest and at the lowest point on the Ferris wheel?
A small car with mass kg travels at constant speed on the inside of a track that is a vertical circle with radius m (Fig. E). If the normal force exerted by the track on the car when it is at the top of the track (point ) is N, what is the normal force on the car when it is at the bottom of the track (point )?
A small remote-controlled car with mass kg moves at a constant speed of m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of m (Fig. E). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point (top of the track)?
A small remote-controlled car with mass kg moves at a constant speed of m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of m (Fig. E). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point (bottom of the track)?
A -kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched; she makes turns each second. The distance from one hand to the other is m. Biometric measurements indicate that each hand typically makes up about of body weight. What horizontal force must her wrist exert on her hand?
On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 55.0 kg, how hard are they pulling on one another?
If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.72, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola described by the equation z = (ω2 / 2g) r2. Hint: Each particle of water on the surface is subject to only two forces: gravity and the normal force due to the water underneath it. The normal force, as always, acts perpendicular to the surface.
A 30 g ball rolls around a 40-cm-diameter L-shaped track, shown in FIGURE P8.53, at 60 rpm. What is the magnitude of the net force that the track exerts on the ball? Rolling friction can be neglected. Hint: The track exerts more than one force on the ball.
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before it broke?
A 5.0 g coin is placed 15 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of μs = 0.80 and μk = 0.50. The turntable very slowly speeds up to 60 rpm. Does the coin slide off?
A 75 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is spherical.
An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ. Find an expression for the angular velocity ω.
Two wires are tied to the 2.0 kg sphere shown in FIGURE P8.45. The sphere revolves in a horizontal circle at constant speed. For what speed is the tension the same in both wires?
A 2.0 kg pendulum bob swings on a 2.0-m-long string. The bob's speed is 1.5 m/s when the string makes a 15° angle with vertical and the bob is moving toward the bottom of the arc. At this instant, what are the magnitudes of the tension in the string?
A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.48 shows that the string traces out the surface of a cone, hence the name. Find an expression for the ball's angular speed ω.