Jeven said:Does anyone know how to plot a displacement-time graph that will give the average velocity of a bouncing ball? The ball bounces 5 times and I would like to know it's average velocity. What equations would I use?
drvrm said:the bouncing ball is a repetitive event and in between the bounces the speed increase -goes to a maximum and then reverses its path. so the displacement time graph should be quadratic in nature.
what is meant by average velocity -i fail to understand but if you take the slope of displacement time graph at various points of time , then a graph of velocity and time can be plotted and one can try to get average velocity.
Jeven said:So what can I do to my graph to make it a linear function?
Can you explain why squaring the time would result in a graph where the gradient is the velocity? Also, would displacement be displacement^2 or stay displacement?drvrm said:a displacement can depend linearly on time only in case of motion with uniform velocity- so the physical event of bouncing ball is not asystem of uniform velocity.
therefore how one can force the system to change its action.
however if you plot displacement with square if time - artificially one can show a linear dependence- for that the initial velocity must be zero.
Jeven said:Can you explain why squaring the time would result in a graph where the gradient is the velocity? Also, would displacement be displacement^2 or stay displacement?
Ok so basically, if I graph time squared and displacement, I WILL get the velocity from the gradient is what you are saying?drvrm said:well one should look at the physical event -
say a ball falling on floor from a
height say h initial velocity =0
so write down equation for displacement - it should be a function of t^2;
again after hitting the floor and bouncing back with finite velocity the displacement will be a function of time and time square.
Jeven said:Ok so basically, if I graph time squared and displacement, I WILL get the velocity from the gradient is what you are saying?
But then I have an equation t^2=2s/a ... so where is the velocity?drvrm said:yes, that's my hint.
for velocity you have the displacement -time graph and if you take slope i.e. rate of change of displacement with time then only you can get velocity -Jeven said:But then I have an equation t^2=2s/a ... so where is the velocity?
drvrm said:for velocity you have the displacement -time graph and if you take slope i.e. rate of change of displacement with time then only you can get velocity -
from any other graph you do not get it as velocity is unique.
Jeven said:I want to find the velocity of a bouncing ball as it bounces 5 times. What do I do?
drvrm said:initially you talked of average velocity-
now you say the velocity which can bounce five times.
so clarify your question again.
Jeven said:My question is what is the average velocity of a ball after 5 bounces?
drvrm said:then you have to work with displacement -time quadratic curve.
if however you have an ideal ball and ideal collision -elastic the one can predict the velocity after any number of bounces as the linetic energy is not lost in bouncing-
i.e. if it is dropped from a height h
the final velocity before the hit will be mgh =1/2 . m v^2 ; so v= sqrt(2.g.h)
and after elastic collision its speed will be same in opposite direction.
so after 5th bounce also it should have the same velocity.
A displacement-time graph of a bouncing ball is a graphical representation of the vertical position of a ball as it bounces over time. The displacement is shown on the y-axis and the time is shown on the x-axis.
The shape of the displacement-time graph of a bouncing ball is directly related to the motion of the ball. The graph will have a series of peaks and valleys, with the peaks representing the maximum height the ball reaches and the valleys representing the ground level. The slope of the graph will also change as the ball bounces, with steeper slopes representing a faster rate of change in displacement.
A displacement-time graph of a bouncing ball can provide information about the height and duration of the bounces, as well as the speed and acceleration of the ball. It can also show the total distance traveled by the ball and the time it takes to complete a full bounce cycle.
The mass of the ball will affect the displacement-time graph by changing the amplitude of the bounces. A heavier ball will have larger peaks and valleys on the graph compared to a lighter ball. The mass of the ball will also affect the speed and acceleration of the ball, which will be reflected in the slope of the graph.
There are several factors that can cause variations in the displacement-time graph of a bouncing ball. These include the surface the ball is bouncing on, the initial height of the ball, air resistance, and the elasticity of the ball. These factors can affect the height, duration, and speed of the bounces, resulting in variations in the shape of the graph.