8. Centripetal Forces & Gravitation

In uniform circular motion, which of the following statements is correct about the acceleration of the object?

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. How fast must the astronaut's head be moving to experience this maximum acceleration?

While fishing, you get bored and start to swing a sinker weight around in a circle below you on a 0.45-m piece of fishing line. The weight makes a complete circle every 0.65 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–20.]

In uniform circular motion, how does the required centripetal force acting on a car change as the car's speed increases while moving around a curve of fixed $r$?

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5–50). If his arms are capable of exerting a force of 1350 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 78 kg and the vine is 4.8 m long.

In uniform circular motion, which of the following quantities are constant?

Which of the following objects is experiencing $\mathrm{centripetal} \mathrm{acceleration}$?

The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10¹¹ m. Find the magnitude of the earth's velocity.

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. What is the tension in the string?

When rounding a curve in uniform circular motion, a car tends to:

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the radial acceleration of the blade tip expressed as a multiple of g?

In uniform circular motion, a particle traveling around a circle at constant speed will experience which type of $acceleration$?

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the linear speed of the blade tip, in m/s?

In uniform circular motion, the tangential speed on the outer edge of a rotating carousel is: