(II) 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.

(III) The position of a particle moving in the xy plane is given by r→ = (2.0m) cos [(3.0 rad/s)t ] i hut +(2.0m) sin [(3.0 rad/s)t ] j hut, where r is in meters and t is in seconds.

(b) Calculate the velocity and acceleration vectors as functions of time.

(III) The position of a particle moving in the xy plane is given by r→ = (2.0m) cos [(3.0 rad/s)t ] i hut +(2.0m) sin [(3.0 rad/s)t ] j hut , where r is in meters and t is in seconds.

(e) Show that the acceleration vector always points toward the center of the circle.

(II) How many revolutions per minute would a 22-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?

(II) 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.] <IMAGE>

A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f.

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(a) Determine the angle θ where the bead will be in equilibrium within the hoop—that is, where it will have no tendency to move up or down along the hoop.

A train traveling at a constant speed rounds a curve of radius 215 m. A lamp suspended from the ceiling swings out to an angle of 18.5° throughout the curve. What is the speed of the train? [Hint: See Example 4–15.]

A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f. <IMAGE>

(b) If ƒ = 2.00 rev/s and r = 25.0cm , what is θ?

A small bead of mass m is constrained to slide without friction inside a circular vertical hoop of radius r which rotates about a vertical axis (Fig. 5–58) at a frequency f.

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(c) Can the bead ride as high as the center of the circle (θ = 90°)? Explain.