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

[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:

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.

 

[berkeman]

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)...

 

[gneill]

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.

 

[CWatters]

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?

 

[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.

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?

 

[gneill]

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.

 

[Sirbastian]

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'?

 

[gneill]

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.

 

[Sirbastian]

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.

 

[gneill]

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

 

[Sirbastian]

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?

 

[gneill]

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.

 

[Sirbastian]

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)

 

[gneill]

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]

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 ?

 

[gneill]

Yes, that looks better.

 

[Sirbastian]

Yes, that looks better.

Thanks a lot for helping me with this problem!

 

[gneill]

Thanks a lot for helping me with this problem!

You're very welcome!