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Chapter 1: Q57E (page 267)

In Example 8.14 (Section 8.5), Ramon pulled on the rope to give himself a speed of 1.10 m/s. What is James鈥檚 speed?

Short Answer

Expert verified

Speed of James is 0.733 m/s.

Step by step solution

01

The given data 

Given that James (mass 90 kg) and Ramon (mass 60 kg) are 20 m apart on a frozen pond.

Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them.

Ramon pulled on the rope to give himself a speed of 1.10 m/s.

Initially, Velocity of center of mass,V=0

mJ=90kgmR=60kgVR=1.10m/s

02

Formulas used

Center of mass is

xi=m1x1+m2x2+m3x3m1+m2+m3

Where mi,sare masses and xi'sare positions.

03

Find James’s speed

Speed of center of mass isv=mRvR+mJvJmR+mJ

0=90kgvJ+60kg1.1m/s90kg/60kg0=90kgvJ+66kg.m/svJ=-66kg.m/s90kgvJ=-0.7333m/s

Hence, speed of James is 0.733 m/s.

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