# Newtons Second Law For A System Of Particles

#### richard karn

1. The problem statement, all variables and given/known data

In figure (a), a 5.4 kg dog stands on a 16 kg flatboat at distance D = 6.1 m from the shore. It walks 2.1 m along the boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore.

2. Relevant equations

Center of mass = (x1m1 + x2m2)/(m1+m2)

3. The attempt at a solution

Since the center of mass cant change i set the two equal.

x1 (position of dog) = 6.1

x2 (center of canoe) = x

(6.1*5.4 + 16x2)/21.4 =

(5.4*(6.1-2.1) + 16(x2+Δcom))/21.4

which gives the change in the center of mass of the boat is .70875 so the dog only moves 2.1-.70875 and starting 6.1 meters away he is 4.70875 but thats wrong

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#### rl.bhat

Homework Helper
When the dog moves towards the shore, the center of gravity of the boat moves away from the boat.Along with that the dog also moves away from the the boat. If x is the distance moves, the equation becomes

[(6.1- 2.1+x)*5.4 + 16*(x2 + x)])/21.4 = the initial center of mass.

Now solve for x.

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