Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadran

Question

Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood.

x =
Consider the fact that the mass is proportional to the area. Can you break the plywood board into two pieces where you would know the center of mass position for each piece, based on the uniform density? What is the expression for finding the center of mass x coordinate of an object based on the masses and x coordinates of the smaller objects that make it up? Since the masses are proportional to the areas, can you write these masses in terms of the area and unknown density? ft y =
Consider the fact that the mass is proportional to the area. Can you break the plywood board into two pieces where you would know the center of mass position for each piece, based on the uniform density? What is the expression for finding the center of mass y coordinate of an object based on the masses and y coordinates of the smaller objects that make it up? Since the masses are proportional to the areas, can you write these masses in terms of the area and unknown density? ft Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood. Consider the fact that the mass is proportional to the area. Can you break the plywood board into two pieces where you would know the center of mass position for each piece, based on the uniform density? What is the expression for finding the center of mass x coordinate of an object based on the masses and x coordinates of the smaller objects that make it up? Since the masses are proportional to the areas, can you write these masses in terms of the area and unknown density? ft Consider the fact that the mass is proportional to the area. Can you break the plywood board into two pieces where you would know the center of mass position for each piece, based on the uniform density? What is the expression for finding the center of mass y coordinate of an object based on the masses and y coordinates of the smaller objects that make it up? Since the masses are proportional to the areas, can you write these masses in terms of the area and unknown density? ft

Explanation / Answer

x=4.66

y=1.66

Center of Gravity for x= (2x2+4x6)/2+4

Center of Gravity for y= (4x1+2x3)/2+4

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