Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum 
Aug 5th 2010, 08:08 AM

#1  Senior Member
Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi
Posts: 137
 graph of motion under gravity
consider a ball is released from a height h, it strikes the ground and rebounces by loosing 10% of its velocity at each rebounces. I have to plot motion of this ball between t1 to t2 sec.
At first strike , it has two vel one with which it strike(v=sq root of 2gh) the ground and one with which it rebounces(i.e. 10%less that v). Suppose at time t ball strikes, then which velocity should I take at time t(vel at which each rebounces or velocity at which it strikes) and why?
Answer is given vel at which it rebounces.
__________________
If science solves one problem, it creates ten other problems.

 
Aug 5th 2010, 01:02 PM

#2  Physics Team
Join Date: Jun 2010 Location: Morristown, NJ USA
Posts: 2,354

At time t=T1 (when the ball hits the ground) it will have a downward (negative) velocity equal to sqrt(2gh), as you said, the instant prior to hitting the ground. Your graph of the ball's position will have a line sloping downward right up to to t = T1. Then it rebounds, with an initial velocity upward of 90% of sqrt(2gh). So the velocity curve is discontinuous at t=T1. If you plot velocity versus time the curve has a big discontinuity at the instant the ball strikes the ground, shifting form v = sqrt(2gh) to +0.9sqrt(2gh) instantaneously.

 
Aug 6th 2010, 01:07 AM

#3  Senior Member
Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi
Posts: 137

you mean right at the time t=T1, plot will have two points ,one at v=sqrt(2gh) other at v=+0.9sqrt(2gh). Can a body have two velocity at the same time?
Thanks
__________________
If science solves one problem, it creates ten other problems.

 
Aug 6th 2010, 05:19 AM

#4  Senior Member
Join Date: Dec 2008 Location: Udupi, Karnataka, India
Posts: 292

Originally Posted by ohm you mean right at the time t=T1, plot will have two points ,one at v=sqrt(2gh) other at v=+0.9sqrt(2gh). Can a body have two velocity at the same time?
Thanks 
No. There is a fraction of a second time delay between rebouncing and striking.

 
Aug 6th 2010, 06:18 AM

#5  Physics Team
Join Date: Jun 2010 Location: Morristown, NJ USA
Posts: 2,354

Take a look at the attached charts, showing the position and velocity of a bouncing ball. Note that at the instant the ball hits the floor it has a big instantaneous change of velocity. This is an idealized graph  such a change in acceleration implies an infinite acceleration at that instant. If you consider what happens to a real ball, it compresses as it hits, taking some amount of time to fully compress. At that instant its velocity is zero. During this compression the ball is deceleraing very rapidly, but its not infinite. Then it starts to spring back, which causes it to accelerate upward.
Last edited by ChipB; Aug 6th 2010 at 06:50 AM.

 
Aug 6th 2010, 08:30 AM

#6  Senior Member
Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi
Posts: 137

sorry! Where is attached chart?
__________________
If science solves one problem, it creates ten other problems.

 
Aug 6th 2010, 08:57 AM

#7  Physics Team
Join Date: Jun 2010 Location: Morristown, NJ USA
Posts: 2,354

Originally Posted by ohm sorry! Where is attached chart? 
Hmm.. you don't see 2 charts embedded in my previous post? I do...
Try this: http://i885.photobucket.com/albums/a...ncing_Ball.jpg 
 
Aug 6th 2010, 09:38 AM

#8  Senior Member
Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi
Posts: 137

sorry! Due to some technical problem in my internet connection, I was unable to see the plot.
I think the graph represents the motion of a body projected verticaly upward with an initial velocity 9.8m/s comes at rest after 1sec. At t= 2sec it has two velocity 10 m/s and 9m/s. Can a body have two velocity at same time ?
__________________
If science solves one problem, it creates ten other problems.

 
Aug 6th 2010, 11:00 AM

#9  Physics Team
Join Date: Jun 2010 Location: Morristown, NJ USA
Posts: 2,354

A real object can not have two velocities at the same time. But then a real object wouldn't instantaneously bounce with infinite aceleration the way the curve shows (recall that infinite acceleration requires infinite force, so it can't happen). So this is more of a math question than a physics question. Basically for the velocity curve that I drew the exact value at t = 2 seconds is undefined. Mathemeticians say that the limit of the curve v as t approaches 2 seconds from the left is 9.8 m/s, and the limit of the curve v as t approaches 2 seconds from the right is +8.82 m/s. Which means depending on how you look at it, the velocity at t= 2 seconds is either value, hence it's undefined. You can only talk about the value of v just slightly before time t = 2, or just slightly after.

 
Aug 7th 2010, 01:38 AM

#10  Senior Member
Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi
Posts: 137

what has made acc infinite here? Since change in vel is finite here, so is it time that has made it infinite. If yes ! Then can't I measur time here. Aslo you have wrote that when ball compress it deaccelerates but it is not infinite here. So what is the factor here that make this difference?
Thanks
__________________
If science solves one problem, it creates ten other problems.

  Search tags for this page  , , , , , , , , , , ,
Click on a term to search for related topics.
 Thread Tools   Display Modes  Linear Mode  