   Chapter 6, Problem 39P

Chapter
Section
Textbook Problem

In a Broadway performance, an 80.0-kg actor swings from a 3.75-m-long cable that is horizontal when he starts. At the bottom of his are, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?

To determine
The maximum height the actors reaches after the upward swing.

Explanation

Given info:

The mass of actor is 80.0kg .

The length of the cable is 3.75m

The mass of the co-star is 55.0kg .

Explanation:

Following figure shows the before and after impact of the actor and co-star.

The mass of actor is 80.0kg .

The length of the cable is 3.75m

The mass of the co-star is 55.0kg .

The Formula to calculate the conservation of energy just before the impact is,

(K.E+P.E)1=(K.E+P.E)i12m1v12+0=0+m1gR12m1v12=m1gR

• (K.E+P.E)1 is the total energy of the actor before impact
• (K.E+P.E)1 is the total energy of the actor initially
• R is the length of the cable
• m1 is the mass of the actor
• m is the mass of co-star
• g is the acceleration due to gravity
• v1 is the speed of actor just before the impact

Rearranging the formula gives the speed as,

v1=2gR

The Formula to calculate the conservation of momentum is,

(m1+m2)v0=m1v1+0

• m2 is the mass of the co-star
• v0 is the speed just after the impact

Rearranging the formula gives the speed,

v0=m1(m1+m2)v1

The Formula to calculate the conservation of energy just after the impact is,

(K

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