Calculate the Movement of a Rowboat When Two People Exchange Seats

[robyfan]

Hey guys, please help.

Two people, one of mass 65kg and the other of mass 40kg, sit in a rowboat of mass 85kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 4.0m apart from each other, exchange seats.
How far will the boat move?
and in what direction will the boat move?

I know it's related to center of mass thing, but couldn't figure out...

 

[HallsofIvy]

Since you know "it's related to center of mass thing", did you try calculating the center of mass? Taking the end at which the 65kg person is sitting to be 0 (let's call that the "bow"), we have a total mass of 65+ 40+ 85= 190 kg, with the 85 kg mass at 2 m (the center of the boat) and the 40 kg mass at 4 m. Taking x to be the center of mass, we have
190x= 0*65+ 2*85+ 4*40= 330 so x= 330/190= 1.74 m from the bow.

After they change places, the 40 kg person is at 0 and the 65 kg person is at 4 m.
Now 190x= 0*40+ 2*85+ 4*65= 430 so x= 430/190= 2.26 m from the bow.

Since there is no external force here, the center of mass of the boat actually stays in the sae place- it is the boat that moves: 2.26-1.74= 0.52 m in the direction of the bow.

 

[M98Ranger]

Hi there,

Sure, I'd be happy to help you with this problem.

To calculate the movement of the rowboat, we can use the principle of conservation of momentum. This principle states that the total momentum of a system remains constant unless acted upon by an external force.

In this scenario, we have a system of three objects - the two people and the rowboat. Initially, the total momentum of the system is zero since everything is at rest.

When the two people exchange seats, the center of mass of the system will shift towards the heavier person (65kg). This means that the boat will move in the direction of the heavier person.

To calculate the distance the boat will move, we can use the equation:

m1v1 + m2v2 = (m1 + m2)v

Where m1 and v1 are the mass and velocity of the first person, m2 and v2 are the mass and velocity of the second person, and v is the velocity of the boat.

Plugging in the values, we get:

(65kg)(0m/s) + (40kg)(0m/s) = (65kg + 40kg)v

Solving for v, we get:

v = 0m/s

This means that the boat will not move at all, since the total momentum of the system remains zero.

I hope this helps to clarify the problem for you. Let me know if you have any other questions. Good luck!