Solving the Stacked Ball Drop Homework

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In summary, the equation is V(small ball) = v(initial) ( 3M -m ) / (M + m) and the ratio is close to 3 if the mass of the small ball is near to 3.
  • #1
Biker
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Homework Statement


A tennis ball has a mass of 75 g that is placed above a basketball has a mass of 590 g. Both are stationary and They were dropped from a height about 1.2 m ( The collisions are perfectly elastic)
1) Calculate the speed of the basketball when it reaches the ground
2) Calculate the height that the tennis ball will reach

Homework Equations


P = m v
F t = m dv

The Attempt at a Solution


Okay, so part one is pretty easy
1) sqrt(2 g 1.2) = 4.89 m/s (Use g as 10)
Now for the 2nd part, It is common that the ratio is 3 ( The speed of the tennis ball is 3 multiplied by the initial speed of it)
However I didnt get that through my calculations ( 2.55)
Here is my solution:
V1: Speed of the basketball
V2: Speed of the tennis ball
1 = v2 -v1/u1 - u2
u1-u2 = v2 -v1
(Without needing to extract this equation through kinetic energy and momentum)
Now the basketball will rebound with the same speed (assuming it is instantaneous) but moving upward
And it will now have a collision with the tennis ball that is moving downward with the same speed
So
4.89--4.89 = v2 - v1
9.79 = v2 - v1
v1 = v2 - 9.79
Now Substitute that in the momentum equation
M* 4.89 - m * 4.89 = M * (v2 - 9.79) + 0.075 v2
Place the value of M and m
and V2 ( Velocity of the tennis ball) will equal to 12.48 m/s.
For the ratio, 12.48/4.89 = 2.55

http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html
Here is the site for a reference about the ratio.
I assume that the mistake might be in that they assume if the top ball hits the bottom one, the bottom one's velocity doesn't change which is a mistake.
And according to my calculations, A ratio of 3 will only result if the m of the tennis ball is 0 which can't happen... Weird

There are various of ways to solve this question, and all of them yield in the same result
 
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  • #2
The analysis at that link assumes the lower ball is much more massive, and it gives the speed ratio 3 as the limit value as the mass ratio tends to infinity. It will never quite equal 3.
 
  • #3
haruspex said:
The analysis at that link assumes the lower ball is much more massive, and it gives the speed ratio 3 as the limit value as the mass ratio tends to infinity. It will never quite equal 3.
Hmm so I got an equation for this type of problems.
V(small ball) = v(initial) ( 3M -m ) / (M + m)

So what they assumed that the M is massive so that the m of the small ball wouldn't affect the ratio that much. So it is basically near 3.
Alrighty, Thanks
 

Related to Solving the Stacked Ball Drop Homework

What is the Stacked Ball Drop Homework?

The Stacked Ball Drop Homework is a physics problem where a certain number of balls are stacked on top of each other and dropped from a certain height. The goal is to determine the final height of the top ball after all the balls have fallen.

What is the purpose of the Stacked Ball Drop Homework?

The purpose of the Stacked Ball Drop Homework is to apply principles of physics, such as conservation of energy and momentum, to a real-life scenario. It also helps students develop problem-solving and critical thinking skills.

How do you solve the Stacked Ball Drop Homework?

To solve the Stacked Ball Drop Homework, you need to first determine the initial potential energy and kinetic energy of the top ball. Then, use conservation of energy and momentum equations to calculate the final height of the top ball.

What are the key concepts involved in solving the Stacked Ball Drop Homework?

The key concepts involved in solving the Stacked Ball Drop Homework include conservation of energy and momentum, gravitational potential energy, and kinetic energy. It is also important to understand the relationship between force, mass, and acceleration.

What are some tips for successfully solving the Stacked Ball Drop Homework?

Some tips for successfully solving the Stacked Ball Drop Homework include carefully reading and understanding the problem, drawing diagrams to visualize the scenario, and breaking down the problem into smaller, manageable steps. It is also helpful to double check your calculations and units to ensure accuracy.

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