Falling Ball Photos

Classical Mechanics Level 1

Percy wants to take photos of a ball bouncing on an elastic floor. He sets his camera to burst mode so that it takes pictures at short, uniform intervals.

If all the photos are merged into one, then how would the merged photo look ?

Assume that the ball does not lose energy but keeps bouncing up to the same height. The ball takes 1 second to drop to the floor, and the camera takes 7 pictures every second.

A B C

10 solutions

Eduardo Zavala
Nov 12, 2017

As the ball is dropped, it initially starts without velocity towards the floor. But it slowly accelerates, each time increasing its speed until it reaches its maximum speed just before hitting the floor. Therefore travelling more distance in 1/7th of a second and making the later pictures more far a apart from each other.

The same goes when bouncing back up, but this time it deaccelerates instead.

Moderator note:

To clear up some confusion from the comments: the problem is written assuming the ball does not lose energy and keeps bouncing up at the same height. Therefore it does not matter when the pictures start being taken - the placements of the ball photos will be identical at each bounce, because it simply returns to where it started and gravity pulls the ball in the exact same way every time.

The question said bounce which insinuates the image capture of the ball after it has touched the ground. bit misleading

sambo jambo - 3 years, 7 months ago

I agree that it's a badly worded question. Someone correct me if I'm wrong, but if the ball takes 1 second to reach the ground and it's a perfectly elastic bounce, (if I'm not mistaken) this means it would take the exact amount of time to go up so by taking 7-second interval pictures, the camera would only capture the ball at the top and bottom, never in between.

A Former Brilliant Member - 3 years, 6 months ago

The camera takes 7 pictures every second, so therefore there would be 7 balls in the merged picture. As de system has zero drag, the energy is conserved so the velocity in the picture near the ground will always me maximum, and in the summit it would be zero.

Again, as the ball moves towards the ground it will keep gaining speed. And when the ball bounces and it goes up it slowly loses speed until it reaches zero. So therefore, the pictures taken would be exactly the same going upwards or going downwards.

Eduardo Zavala - 3 years, 6 months ago

Since the ball is not loosing velocity and goes to the same height every time I would assume it would be a zero gravity enviroment and hence B would be the "correct" answer?

Laurits Bertelsen - 3 years, 6 months ago

Its not a zero gravity enviroment, its a zero drag enviroment (since the ball does not lose energy). If it were a zero gravity enviroment the ball would just float.

Eduardo Zavala - 3 years, 6 months ago

"does not lose energy" is an impossible proposition because you are assuming a damped oscillation anyway, A can not be the answer.

Parthapratim Chakravorty - 3 years, 6 months ago

On the note it says that the ball doesn't lose energy, In B all of the balls had the same distance so I thought it was B. I think guess and check works best for this. How does this work? I would rate this problem a 10 because I don't know much about physics. At first I felt like it was easy but then I realized that it was again one of those physics problems that I don't know.

Lucia Tiberio - 3 years, 6 months ago

One problem is that is does say he is recording the bouncing. In saying this, the implication would be that the ball was already dropped and is bouncing up from the elastic floor. In this case, C should be right.

Michael K. - 3 years, 6 months ago

Md Mehedi Hasan
Nov 12, 2017

we know for backward motion,if a object starts without velocity, it maintains this formula,

$h\propto v^2$

It means, for time being constant, velocity depends on height. So if I dropped a ball, it's velocity will increase in a constant acceleration. So when the ball was in starting position it's velocity was little. And when it was floor touching, it's velocity was much for an equivalent time. So the answer is A.

Why not D(a new picture) in case the shot is initiated just when the ball starts bouncing back. In the sdtatement of the problem npyhing is mentioned about starting of the Camera as well as duration of the operation of the Camera.

Satyabrata Biswas - 3 years, 6 months ago

For upward motion we also get same picture A. Because when a object starting moving after bouncing, it's velocity will be decreasing for a constant acceleration which is gravitational acceleration. So again for upward motion, the velocity was much when it was floor leaving and the velocity was little when it was in maximum height.

Md Mehedi Hasan - 3 years, 6 months ago

Kevin Tong
Nov 13, 2017

Gravity is an acceleration constant. Therefore, as the ball goes down, it accelerates, meaning its velocity increases, and in turn, so does the distance over intervals of equal time.

The part that throws me off is the elastic floor and not knowing the weight of the ball. Picture a bowling ball hitting a trampoline... you'd have a bunch of close together shots at the top AND bottom (as it stretches the "floor" then shoots back up and slows down again at the top) My answer is D - "none of the above"

Steve Anderson - 3 years, 6 months ago

correct! A cannot be the answer, though C is still closer as the ball goes through a damped oscillation here.

Parthapratim Chakravorty - 3 years, 6 months ago

Dc Bray
Nov 17, 2017

Newton's Laws of Motion applies here, particularly 1 and 2.

Sanket Jain
Nov 16, 2017

Due to Gravitational accelerates, its speed increases so cover more distance in 1/7th of a second and making the later pictures more far a apart from each other.

Chloe Peng
Nov 16, 2017

if you bounce a ball and take shots of it, it will look like A

Suraj Swaminathan
Nov 16, 2017

As the ball moves up, gravity acts on it which slows the speed of the ball and thereby decreases the distance traveled each second. Therefore the photo burst will look like that of A.

Faffywaffy Rhodes
Nov 14, 2017

The ball is fastest after it initially bounces off the floor, the camera will capture more images of the ball as it starts to lose it's momentum to gravity while it's up in the air about to fall down.

I agree. If the images are merged, the camera would capture the exact reverse of the acceleration due to falling as the ball is accelerating off the elastic floor. There should be 12 images with balls closer together at both the top and bottom with more spaced balls in the center.

Vince Brown - 3 years, 6 months ago

Wasim Sk
Nov 14, 2017

It starts with a free fall by slowly increasing its velocity as the intervals between the picture taken is constant the distance travelled between the intervals increases as the speed increases. Thank you.

Rishabh Singh Chauhan
Nov 14, 2017

Well in simple words as the ball goes up it has less velocity so the camera can take more pictures.

Falling Ball Photos

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