How to calculate the mass of a ball based on a video

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Homework Help Overview

The discussion revolves around calculating the mass of a ball based on its motion observed in a video. Participants are exploring the relationship between force, mass, and acceleration, particularly in the context of a ball and a cart system influenced by gravity and possibly other forces.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for additional information, such as the spring constant and the initial conditions of the system. There are attempts to relate the mass of the ball to the observed accelerations of the cart and the falling weight. Questions arise regarding the significance of air resistance and the trajectory of the ball.

Discussion Status

Several participants have provided insights and suggestions for approaching the problem, including deriving equations based on the forces involved. There is ongoing exploration of the relationships between the masses and accelerations, with some participants questioning the calculations and seeking clarification on algebraic manipulations.

Contextual Notes

Participants are working under the constraints of a homework assignment, which limits the information they can use. There is an emphasis on deriving equations and understanding the underlying physics without directly providing solutions.

Sirbastian
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Homework Statement


I would like to know how I calculate mass of a ball based on a video. I can measure the speed of the ball at any point using Coach 3 (computer program). I know g=9.81m/s2 for the rest i don't know anything. I would like to know the way to calculate the mass of the ball in this video:


Homework Equations


F=m*a ?
E=mc2 ?

The Attempt at a Solution


I have no clue, i only know the velocity of the ball.

Thanks in advance for reacting to this thread.
 
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Sirbastian said:

Homework Statement


I would like to know how I calculate mass of a ball based on a video. I can measure the speed of the ball at any point using Coach 3 (computer program). I know g=9.81m/s2 for the rest i don't know anything. I would like to know the way to calculate the mass of the ball in this video:


Homework Equations


F=m*a ?
E=mc2 ?

The Attempt at a Solution


I have no clue, i only know the velocity of the ball.

Thanks in advance for reacting to this thread.

Welcome to the PF.

It would seem that you would need to know the spring constant of the spring mechanism below the ball, and the initial deflection of the mechanism. Once in flight, all masses will behave the same (ignoring air resistance)...
 
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The trajectory of the ball may be a distraction. Perhaps the key is that the ball and cart start out as one object accelerating together, then become separated leaving only the cart to accelerate horizontally. I think you'd need to know something about the mass of the falling weight and perhaps details of the pulley if its moment of inertia is significant. You'd also need to know if any friction values are significant.
 
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This is unlikely to work in practice but...

If you know the horizontal velocity at various points in time you can work out how fast it decelerates due to air resistance. Then if you know the diameter of the ball I suppose you might be able to estimate it's mass using aerodynamics. However I don't think the answer would be very accurate.

My money is on it being very light weight. Something like a painted table tennis ball perhaps?
 
gneill said:
The trajectory of the ball may be a distraction. Perhaps the key is that the ball and cart start out as one object accelerating together, then become separated leaving only the cart to accelerate horizontally. I think you'd need to know something about the mass of the falling weight and perhaps details of the pulley if its moment of inertia is significant. You'd also need to know if any friction values are significant.

Okay, so I now know the mass of the falling weight is 0.5kg and it falls at an acceleration rate of 1.8m/s2 before ejecting the ball, and at an acceleration rate of 3.2m/s2 after the ball is ejected. How can I calculate the mass of the ball with this information?
 
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Sirbastian said:
Okay, so I now know the mass of the falling weight is 0.5kg and it falls at an acceleration rate of 1.8m/s2 before ejecting the ball, and at an acceleration rate of 3.2m/s2 after the ball is ejected. How can I calculate the mass of the ball with this information?
Start by finding an equation for the acceleration for the simple case where there are two masses: M on the table and m falling. You've got two scenarios then, one where the mass M would represent both the cart and the ball and one where it is the cart alone. Determine M for each case.
 
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gneill said:
Start by finding an equation for the acceleration for the simple case where there are two masses: M on the table and m falling. You've got two scenarios then, one where the mass M would represent both the cart and the ball and one where it is the cart alone. Determine M for each case.
Thanks for the reply, do you happen to know 'this equation'?
 
Sirbastian said:
Thanks for the reply, do you happen to know 'this equation'?
It's the one you'll have to derive yourself. After all, this is your homework. :smile:

As usual, draw Free Body Diagrams and identify the forces. Proceed from there.
 
gneill said:
It's the one you'll have to derive yourself. After all, this is your homework. :smile:

As usual, draw Free Body Diagrams and identify the forces. Proceed from there.
I want to say thank you for your support, I figured out how to do it (or at least how I think the problem is solved):

m1 = xkg
m2 = 0.5kg
a1 = 1.8m/s2
a2 = 3.2m/22

So the amount of force from the falling weight is 0.5x9.81=4.9N
F=m1 *a ---> 4.9 = x*1.8 ---> 4.9/1.8=2.7kg (before launch of the ball)
F=m1 *a ---> 4.9 = x*3.2 ---> 4.9/3.2=1.5kg

2.7-1.5 = 1.2kg = the mass of the ball.
 
  • #10
Careful, there are two masses accelerating: One force accelerates the total mass.
 
  • #11
gneill said:
Careful, there are two masses accelerating: One force accelerates the total mass.
I see, so:
4.9 = (m1+m2)*1.8 = 0.9m1 --> 4.9/0.9= 5.4kg
and
4.9 = (m1+m2)*3.2 = 1.6m1 --> 4.9/1.6= 3kg

5.4-3 = 1.4kg = the mass of the ball

Is this the right way the solve this problem?
 
  • #12
I'm not sure how you're carrying out your calculations. Can you show one in detail using symbols only? Let F be the force due to gravity on the falling weight, a be the measured acceleration.
 
  • #13
gneill said:
I'm not sure how you're carrying out your calculations. Can you show one in detail using symbols only? Let F be the force due to gravity on the falling weight, a be the measured acceleration.

I did something wrong here (again),
m2 is the mass of the falling weight
m1 is the mass of the cart (+ the mass of the ball on t=x)

it should be:

F=m*a --> m2*g = 0.5*9.81= 4.9N
Fres = m*a ---> 4.9N = (m2+m1)*a1 --->
4.9-m2 = m1*a1 --->
(4.9-m2)/a1= m1(t=x)

Fres = m*a ---> 4.9N = (m2+m1)*a2 --->
4.9-m2 = m1*a2 --->
(4.9-m2)/a2 = m1(t=y)

m1(t=x) - m1(t=y) = m3 (mass of the ball)
 
  • #14
Sirbastian said:
I did something wrong here (again),
m2 is the mass of the falling weight
m1 is the mass of the cart (+ the mass of the ball on t=x)

it should be:

F=m*a --> m2*g = 0.5*9.81= 4.9N
Fres = m*a ---> 4.9N = (m2+m1)*a1 --->
4.9-m2 = m1*a1 --->
How did you move m2 to the left hand side? Note that it is multiplied by a1 on the right hand side. Also, you end up subtracting a mass from a force, so the units don't match. You need to do a bit more algebra to isolate m1 properly.
 
  • #15
Sirbastian said:
I did something wrong here (again),
m2 is the mass of the falling weight
m1 is the mass of the cart (+ the mass of the ball on t=x)

it should be:

F=m*a --> m2*g = 0.5*9.81= 4.9N
Fres = m*a ---> 4.9N = (m2+m1)*a1 --->
4.9-m2 = m1*a1 --->
(4.9-m2)/a1= m1(t=x)

Fres = m*a ---> 4.9N = (m2+m1)*a2 --->
4.9-m2 = m1*a2 --->
(4.9-m2)/a2 = m1(t=y)

m1(t=x) - m1(t=y) = m3 (mass of the ball)

So when 4.9N = (m2+m1)*a1 ---> m1(t=x) = (4,9/a1) - m2 and
4.9N = (m2+m1)*a2 ---> m1(t=y) = (4,9/a2) - m2 ?
 
  • #16
Yes, that looks better.
 
  • #17
gneill said:
Yes, that looks better.
Thanks a lot for helping me with this problem!
 
  • #18
Sirbastian said:
Thanks a lot for helping me with this problem!
You're very welcome!
 

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