Mass of a ball with different density

In summary, the problem involves a solid ball with density p1 and radius R, with a smaller ball of radius R/2 and density p2 placed inside it. The task is to find the new mass of the larger ball by subtracting the mass of the smaller ball and adding back the mass of the material inside it. The conversation then shifts to finding the period time T for the movement of the ball on a surface with friction.
  • #1
asi123
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0

Homework Statement



Hey guys.
Look at this one, I have a ball with density p1 and radius R. Inside the ball they dig another ball with radius R/2 and fill it up with material that has density p2. My question is, why does the mass "m" equals to what they wrote in the answer (marked with red)? why do I need to subtract the densitys in order to find the new mass?
10x.

Homework Equations





The Attempt at a Solution

 

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  • #2
M is the mass of a solid ball of density p1 and radius R. But you've cut out a ball of radius R/2 and replaced it with a different density. To find the new mass of the ball: subtract the mass you cut out (p1) and add back the mass you replaced it with (p2).
 
  • #3
Still, this is what I got (in the pic).
 

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  • #4
Looks good to me.
 
  • #5
Ok, so do you know maybe what is that expression I marked in red could be?
 
  • #6
asi123 said:
Ok, so do you know maybe what is that expression I marked in red could be?
Beats me. Where did you get it?

I assume that you've presented the problem accurately: Find the new mass of the large ball?
 
  • #7
Oh, sorry, I forgot to post the entire problem...:blushing:
Anyway, they did what they did with ball, then, they put it on a surface with friction, diverted it a bit and then release (by a "bit" I mean that the angle is really small). the question is to find the period time T of the movement of the ball.
 

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1. What is mass and how does it differ from density?

Mass is a measure of the amount of matter in an object, while density is a measure of how tightly packed the matter is within that object. In other words, mass is the total quantity of material present, while density is the concentration of that material within a given volume.

2. How does the density of a ball affect its mass?

The density of an object is directly proportional to its mass. This means that as the density of a ball increases, so does its mass. Similarly, as the density decreases, so does the mass.

3. Can a ball have the same mass but different densities?

Yes, it is possible for a ball to have the same mass but different densities. This can occur if the size and shape of the ball are different, but the amount of matter (or mass) remains the same.

4. How is the mass of a ball with different densities measured?

The mass of a ball with different densities can be measured using a scale or balance. The ball is placed on the scale and the reading is taken. This gives the total mass of the object, regardless of its density.

5. Why is it important to know the mass of a ball with different densities?

Knowing the mass of a ball with different densities is important in understanding its physical properties and how it will behave in certain situations. Mass is also an important factor in calculating other properties such as momentum and kinetic energy.

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