Calculate the centre of mass of the object shown below

In summary, the object has a center of mass that is located at the lower left on the page, and if you break it up into four squares, the center of mass for each square is at the lower right corner of that square. The center of mass for the entire object is located at the center of the page.
  • #1
LadyTwi
8
0
I have a few questions that are driving me nuts.

First: Calculate the centre of mass of the object shown below. Assume that the mass density is uniform. Place the origin, O, at the lower left. If the positive x-axis points to the right along the page, what is the x coordinate of the centre of mass, in terms of a? If the positive y-axis points up along the page, what is the y coordinate of the centre of mass, in terms of a?

http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype15/CentreOfMass4.gif

So, this object could be broken up into four squares right? Would finding the center of mass of each square help?

Second: A 7490 kg rocket is set for vertical firing from the Earth's surface. If the exhaust speed is 1550 m/s, how much gas must be ejected each second in order for the thrust to be equal to the weight of the rocket? How much gas must be ejected each second to give the rocket an initial upward acceleration of 16 m/s2?

I already found how much gas must be ejected for the thrust to equal the weight of the rocket: 47.36 kg

I'm unsure of how to relate the acceleration to the problem. It's probably so obvious. XD
 
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  • #2
So, this object could be broken up into four squares right? Would finding the center of mass of each square help?

Yes, it will help.
How much gas must be ejected each second to give the rocket an initial upward acceleration of 16 m/s2?

I already found how much gas must be ejected for the thrust to equal the weight of the rocket: 47.36 kg

I'm unsure of how to relate the acceleration to the problem. It's probably so obvious.
Use: F=ma. F is the resultant of the thrust (upward) and gravity (downward). You can calculate the thrust and then the mass of gas from it.

ehild
 
  • #3
All right, I got both answers. Thanks!
 

What is the definition of center of mass?

The center of mass of an object is the point at which the mass of the object is evenly distributed in all directions. It is the average position of all the mass in the object.

How do you calculate the center of mass of an object?

To calculate the center of mass, you need to find the weighted average of the individual masses in the object. This can be done by multiplying the position of each mass by its respective mass and then dividing by the total mass of the object.

What information do you need to calculate the center of mass?

To calculate the center of mass, you need to know the position and mass of each individual component of the object. This information can be obtained through measurements or given in the problem statement.

Why is the center of mass important?

The center of mass is important because it helps us understand how an object will behave when it is subject to external forces. It also gives us a reference point for determining the rotational motion of an object.

How does the shape of an object affect its center of mass?

The shape of an object affects its center of mass by changing the distribution of mass within the object. Objects with more mass concentrated towards one end will have a center of mass closer to that end, while objects with uniform mass distribution will have a center of mass in the geometric center.

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