(II) A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig. 7-39), each of which is a cube of length I Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.

Solution 51P:

We have to determine the location of center of gravity(center of mass) of the systems in the horizontal.

Step 1 of 3</p>

Concept:

Center of mass(CM) of a body is an imaginary point at which whole mass of the body is supposed to be concentrated.We consider that the net force acts on the centre of mass of body, insteads of considering that it acts on each and every point on the body for simpler calculation and this is one of the importance of application of CM.

Center of the gravity of a body is an imaginary point at which whole weight of the body is acting vertically downward. For the body with uniform distribution and placed in uniform gravitational field, the center of mass of the body coincide with center of gravity.

Step 2 of 3</p>

Let the mass of each case be and each cube case is having the side .

For finding the x and y coordinates of the center of mass of the system in horizontal plane, we consider the origin at the point of intersection of x-axis and y-axis respectively as shown in figure below.