Physics- center of mass problem ?

In summary, there is a figure given with an extended object and its coordinates of the center of mass are (L/4, -L/5). The question asks for the coordinates of m1, assuming m1 = 4 kg, m2 = 2 kg, and m3 = 3 kg. The user provides a calculation for the coordinates, with x = -9L/16 and y = -L/10, and requests for any errors to be pointed out. Another user asks for clarification on what axis is being used to calculate moments, and provides a formula for calculating the center of mass about the x axis. Finally, someone asks for help with calculating the magnitude of two perpendicular forces with a resultant of 100
  • #1
J.live
95
0

Homework Statement



The coordinates of the center of mass for the extended object shown in the figure are (L/4, −L/5). What are the coordinates of m1? (Assume m1 = 4 kg, m2 = 2 kg, and m3 = 3 kg. Use any variable or symbol stated above as necessary.)

Here is the diagram : http://tinypic.com/view.php?pic=33da26e&s=7[
Can someone check my work?

4(x,y) + 3(-L/4,-3L/10) + 2(-3L/4,-L/4) = 0

-( 4x,4y) +(-3L/4,9L/10) + (-3L/2,-L/2) = 0

-4x - 3L/4 - 3L/2 = 0

-4y + 9L/10 - L/2 = 0

-4x = 9L/4

-4y = 4L/10

x = -9L/16

y = -L/10

P.S. please let me know what errors I made, if any.

Thanks.
 
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  • #2
Help :/?
 
  • #3
What axis have you chosen for calculating the moments of the masses? For the c.m. about the x axis, it's m1y1 + m2y2 + m3y3 = (m1 + m2 +m3) Y_c.m. , where the y1, y2, anmd y3 terms are the respective distances from the x axis, and Y_c.m. is given as -L/5.
 
  • #4
two forces whose resultants is 100N perpendicular to each other,if one of them makes an angle of 60 degrees with the resultants,calculate its magnitude?
 
  • #5
seansharpzy said:
two forces whose resultants is 100N perpendicular to each other,if one of them makes an angle of 60 degrees with the resultants,calculate its magnitude?
Sean, please post this as a new topic and show an attempt at a solution. Thanks.
 

Related to Physics- center of mass problem ?

1. What is the center of mass in physics?

The center of mass in physics refers to the point at which the entire mass of a body can be considered to be concentrated for the purpose of performing calculations. It is the average position of all the mass in a system.

2. How is the center of mass calculated?

The center of mass is calculated by taking the weighted average of the positions of all the individual particles in a system. The formula for calculating the center of mass is:
xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where x is the position and m is the mass.

3. Why is the center of mass important in physics?

The center of mass is important in physics because it helps to simplify complex systems and allows us to analyze the motion of objects. It also plays a key role in understanding concepts such as torque, angular momentum, and collisions.

4. How does the center of mass affect the stability of an object?

The location of the center of mass is directly related to the stability of an object. In general, the lower an object's center of mass, the more stable it will be. This is why objects like a pyramid or tripod are more stable than a tall, narrow object like a pencil.

5. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This is often the case with irregularly shaped objects, where the center of mass may be located in empty space rather than within the physical boundaries of the object. However, the center of mass will always lie along the line of symmetry of an object, even if it is outside of the object itself.

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