Solving the Boat Movement After Romeo & Juliet's Kiss: 0.7m

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Juliet moves 2.7m across the boat to kiss Romeo, who together with the boat weighs 157 kg, while Juliet weighs 55 kg. The key to solving the problem lies in understanding that the center of mass of the entire system (boat, Romeo, and Juliet) must remain stationary due to the absence of horizontal forces from the water. As Juliet moves, the boat must shift in the opposite direction to maintain the center of mass, resulting in the boat moving 0.7m. The calculations confirm that the net force on the system is zero, allowing for a straightforward determination of the boat's movement. This understanding clarifies how the system's dynamics work when one mass moves within it.
Satoy
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I've got most of the problem completed but I need a little help on the last little bit. Julet moves across the boat 2.7m to romeo to give him a kiss. Romeo and the boat weigh 157 kg and Julet weighs 55 kg. How far does the boat move. The boat is at rest before hand.

The answer is .7m and I have no idea how the book got that.
 
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Hint: If you assume that the water exerts no (horizontal) force on the boat, then the center of mass of the "boat + Romeo + Juliet" cannot move.
 
Oh ok you just put me in the right state of mind, I got it now.
 
Let me see if I am right the F to move Juliet needs to be applyed to the total system right?
 
Yes.From there,the answer is simple to find.

Daniel.
 
Satoy said:
Let me see if I am right the F to move Juliet needs to be applyed to the total system right?
Not sure what you are saying here. The net force on the total system is zero.

Think like this. Before Juliet moves, the center of mass of the total system is at some point on the boat. Mark that point with an X. When Juliet moves, where is the new center of mass with respect to that X?
 

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