Calculating Center of Mass: Rowboat with Kids | Find x Distance

[shenwei1988]

When empty, a 166 kg rowboat is symmetrical. A boy of mass 70.5 kg sits 2.1 m from the center of mass of the rowboat toward the front of the boat, and a girl of mass 68.8 kg sits 2.38 m from the center of mass of the rowboat toward the rear of the boat. Find x, distance from center mass of the emptyt rowboat to the center of mass of the rowboat-plus-kids system.


Xcm=(M1X1+M2X2)/(M1+M2)



what's the center mass of the empty rowboat?


(70.5*2.1+68.8*2.38)/(166+70.5+68.8) is it the center of mass of the rowbot-plus-kids system??

please help me . thanks a lot

 

[BigJDubs]

. No, that is not the center of mass of the rowboat-plus-kids system. To find the center of mass of the rowboat-plus-kids system, you need to use the formula given above. Substitute in the masses and distances from the center of mass of the empty rowboat for each of the children: Xcm = (70.5*2.1 + 68.8*2.38) / (166 + 70.5 + 68.8) Xcm = 2.26 m

 

[Moetasim]

The center of mass of the empty rowboat would be at the midpoint of the boat, since it is symmetrical. So, the center of mass would be at 0 meters from the center of the boat.

To find the center of mass of the rowboat-plus-kids system, we can use the formula provided: Xcm=(M1X1+M2X2)/(M1+M2). In this case, M1 would be the mass of the boy (70.5 kg) and X1 would be his distance from the center of mass (2.1 m). Similarly, M2 would be the mass of the girl (68.8 kg) and X2 would be her distance from the center of mass (2.38 m).

So, Xcm=(70.5*2.1+68.8*2.38)/(70.5+68.8)=2.24 m

Therefore, the center of mass of the rowboat-plus-kids system would be 2.24 m from the center of the boat. This means that the distance x from the center of mass of the empty rowboat to the center of mass of the rowboat-plus-kids system would be 2.24 m.