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

• Sirbastian
In summary, to calculate the mass of a ball based on a video, you will need to know the mass of the falling weight, as well as its acceleration before and after ejecting the ball. Using these values and the equation F=m*a, you can calculate the mass of the ball at the moment it is ejected.
Sirbastian

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:

F=m*a ?
E=mc2 ?

The Attempt at a Solution

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

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:

F=m*a ?
E=mc2 ?

The Attempt at a Solution

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

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)...

Sirbastian
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.

berkeman
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?

CWatters
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.

CWatters
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.

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.

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.

Careful, there are two masses accelerating: One force accelerates the total mass.

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?

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.

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)

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.

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 ?

Yes, that looks better.

gneill said:
Yes, that looks better.
Thanks a lot for helping me with this problem!

Sirbastian said:
Thanks a lot for helping me with this problem!
You're very welcome!

1. How do I determine the mass of a ball based on a video?

To calculate the mass of a ball based on a video, you will need to use the formula: mass = density x volume. The density of the ball can be determined by researching the material it is made of, and the volume can be measured by using the dimensions of the ball.

2. Can I use any type of video to calculate the mass of a ball?

Yes, you can use any type of video as long as you have accurate measurements of the ball's dimensions and can determine the material it is made of. However, it is recommended to use a high-quality video with clear visuals for more accurate calculations.

3. How many data points do I need from the video to calculate the mass of the ball?

You will need at least two data points from the video to calculate the mass of the ball. These data points should include the dimensions of the ball and the time it takes for the ball to fall a certain distance.

4. Can I use this method to calculate the mass of any type of ball?

Yes, this method can be used to calculate the mass of any type of ball as long as you have accurate measurements and can determine the material it is made of. However, the accuracy may vary depending on the quality of the video and the precision of the measurements.

5. Is there a more accurate way to calculate the mass of a ball?

Yes, there are other methods that can be used to calculate the mass of a ball, such as using a scale or using the buoyancy principle. However, calculating the mass based on a video can still provide a fairly accurate estimate if done correctly.

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