Two skaters, one with mass65kgand the other with mass 40kg, stand on an ice rink holding a pole of length 10mand negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 40kgskater move?

Short Answer

Expert verified

The distance covered by the skater m2 from the center of mass of the system isx=6.2m.

Step by step solution

01

Listing the given quantities

The mass of the one skater is m1=65kg.

The mass of the second skater ism2=40kg.

The length of the pole isI=10m.

02

Understanding the concept of center of mass

We can use the concept of center of mass of the system. When skaters are pulling each other, the center of mass of the system will not move. Therefore, skaters will meet at the center of mass irrespective of pull from both the skaters.

Formula:

Rcm=m1r1+m2r2m1+m2

03

Calculations of the height of the center of mass

The center of mass of the system does not move. The skaters are meeting at the center of mass. Consider the m2meets distance x from the center of mass.

Substitute the values in the equation (i)

0=(65kg)(10m-x)+(40kg)(-x)65kg+40kg(65kg)(10m-x)-(40kg)(x)=0(65kg×10m)-(65kg×x)=(40kg)(x)(65kg×10m)=(40kg)(x)+(65kg×x)(65kg×10m)=(40kg+65kg)(x)x=(65kg×10m)(40kg+65kg)=6.2m
The distance covered by the skater m2from the center of mass of the system is x=6.2m

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