Question

A square uniform raft, 18.0m by 18.0m, of mass 6290kg, is used as a ferryboat. If three cars, each of mass 1132kg, occupy the NE, SE, and SW corners, determine the CM of the loaded ferryboat. Use east as the positive x-axis, north as the positive y-axis and the centre of the raft as the origin.

Answer 1

First step draw a diagram. Now there are four masses: the raft itself and the three cars.

You can consider the mass of the ferry to be all at its geometric center.

Hence each mass now has a number associated with it: it's mass, call them m1, m2, m3, m4. And they also have located with them a location vector, call them v1 ... v4.

The center of mass is the weighted average of those four vectors, weighted by the mass for each. That is the center of mass is located at:
\[ CM = \frac{m_1v_1 + m_2v_2 + m_3v_3 + m_4v_4}{m_1 + m_2 + m_3 + m_4} \]

This is why you've been given coordinate axes in this problem: to help you figure out the four location vectors.

Therefore, to solve this problem:
- find each of these vectors
- then calculate the CM using the formula above.

Answer 2

can you show me the steps please?

Answer 3

have you drawn the diagram, showing the location of the three cars and the location of the center of mass of the raft? Start there.

Answer 4

yes i have that done

Answer 5

ok, what is the position of the car in the NE corner? Call that v1, what is that in cartesian coordinates?

Answer 6

i dont understand what you mean

Answer 7

In your diagram you have x and y axes yes? Where is the origin of that coordinate system?

Answer 8

would it be (0,18) is that what you mean?

Answer 9

Step back. Where is the origin of the coordinate system, the point where the two axes meet? You're told to put it in the center of the raft.

Now, that being the case, what are the coordinates of the NE corner?

Answer 10

(-9, 9) ?

Answer 11

am i screwing this up completely?