Center of gravity (x and y coordinates) of mechinist's square

In summary, the machinist's square consists of a thin, rectangular blade connected to a rectangular handle. The task is to determine the x and y coordinates of the center of gravity. The equations used are x_cg = (m_1 * x_1)+(m_2 * x_2).../(m_1+m_2+...) and y_cg = (m_1 * y_1)+(m_2 * y_2).../(m_1+m_2+...). However, the given numbers used to calculate the center of gravity were incorrect as the cm for the components were not taken into consideration. It is important to carefully consider all quantities before performing calculations in order to get the correct answer.
  • #1
chinnie15
29
0

Homework Statement


The machinist's square shown in the figure consists of a thin, rectangular blade connected to a rectangular handle. Determine the x and y coordinates of the center of gravity. Let the lower corner be x=0, y=0.
problem53.png


Homework Equations


x_cg = (m_1 * x_1)+(m_2 * x_2).../(m_1+m_2+...)
y_cg = ...... (same thing, but y)

The Attempt at a Solution

p

I have gotten an answer, but it is not matching up with the back of the book. Here are the numbers I used to get my answer:

x_1 = 4cm
x_2 = 12cm
y_1 = 11cm
y_2 = 3.0cm

for x_cg I have: [(4cm*40g)+(12cm*80g)] / (40g+80g)= 9.3cm
for y_cg I have: [(11cm*40g)+(3.0cm*80g)] / (40g+80g)= 5.67cm

What did I do wrong? Thank you for any help! :smile:
 
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  • #2
You did not think about where the cm for the components were. You simply took the given dimensions and started plugging in numbers. Go back and think about these quantities carefully before you start calculating. Then you will get the right answer.
 

FAQ: Center of gravity (x and y coordinates) of mechinist's square

1. What is the center of gravity (x and y coordinates) of a mechanic's square?

The center of gravity of a mechanic's square refers to the point where the weight of the square is evenly distributed. This point can be found by balancing the square on a narrow edge or by using a plumb line to determine the midpoint of the square.

2. Why is it important to know the center of gravity of a mechanic's square?

Knowing the center of gravity of a mechanic's square is important because it allows for more precise and accurate measurements. It also helps in determining the stability and balance of the square, which is crucial for its proper functioning.

3. How do you calculate the center of gravity of a mechanic's square?

The center of gravity of a mechanic's square can be calculated by using the formula: x = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn), where x is the x-coordinate, w is the weight, and x1, x2, ... xn are the x-coordinates of each part of the square.

4. Can the center of gravity of a mechanic's square change?

Yes, the center of gravity of a mechanic's square can change if the distribution of weight within the square is altered. For example, if a heavier object is added to one side of the square, the center of gravity will shift towards that side.

5. How does the center of gravity of a mechanic's square affect its stability?

The center of gravity of a mechanic's square plays a crucial role in its stability. If the center of gravity is located outside the base of the square, it will be unstable and prone to tipping over. Therefore, it is important to ensure that the center of gravity is within the base of the square for optimal stability.

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