   Chapter 7, Problem 64AP

Chapter
Section
Textbook Problem

A stuntman whose mass is 70 kg swings from the end of a 4.0-m-long rope along the arc of a vertical circle. Assuming he starts from rest when the rope is horizontal, find the tensions in the rope that are required to make him follow his circular path (a) at the beginning of his motion, (b) at a height of 1.5 m above the bottom of the circular arc, and (c) at the bottom of the arc.

a)

To determine
The tension required for the stuntman to follow the circular path at the beginning of the motion.

Explanation

Given info: The mass of the stuntman is 70kg . The length of the rope is 4.0m . The stuntman starts from rest when the rope is horizontal.

Explanation:

The situation of the problem is shown in the following figure.

The resultant of the tension force and the radial component of the weight of the stuntman is providing the required centripetal acceleration.

Tmgcosθ=mv2r

• r is the length of the rope
• T is the tension in the rope
• m is the mass of the stuntman
• θ angle made by the rope with the vertical
• v is the velocity of the stuntman

The tension in the rope will be,

T=mgcosθ+mv2r

Apply conservation of energy from when the rope was horizontal to when the rope is making angle θ with the vertical

(KE+PE)θ=90°=(KE+PE)θ

The kinetic energy at the horizontal position is zero. Potential energy at the bottom of the arc is zero

b)

To determine
The tension required for the stuntman to follow the circular path when the stuntman is 1.5m from the bottom of the arc.

c)

To determine
The tension required for the stuntman to follow the circular path at the bottom of the arc.

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