The Determination of the Ideal Velocity of the Bouncing Ball Essay Sample
A difficult gum elastic ball is dropped from remainder. It falls to the concrete floor and bouncinesss back up ALMOST to its initial tallness. A gesture sensor is mounted on the ceiling straight above the ball. confronting down. So. the positive way — the away-from-the-detector way — is downward. Pull the place. speed. and acceleration graphs.
Since traveling downward is a positive way. is the speed positive when the ball falls. 0 when it hits the land. and so negative when it moves up? Is the accerlation positive ( 9. 8 ) as the ball falls. really positive when it hits the land. and so neg ( about -9. 8 ) when it moves up? Keep in head that the job says: the ball bounces back up ALMOST to its initial tallness. Besides. delight assist me with understanding how the place graph should look like. If there is any manner that you could pull me the graphs. that would truly be helpful. Thank you! You’re midway right.
Velocity will be positive as the ball falls. nothing on impact. negative on the manner up. and nothing once more at culmination.
Acceleration. nevertheless. is invariably 9. 8 m/s?…the force of gravitation does non alter as the ball moves.
For your graphs. acceleration will be a horizontal line at y=9. 8
Velocity will be a broken sinusiod ( hovering ) that starts at the beginning and rises to a maximal. On each impact with the land. the graph will drop directly down to a lower limit. so rise bit by bit through nothing back up to its following upper limit which will be less than the old upper limit. This will reiterate until the ball is at remainder.
Position will be a smooth sinusiod that begins at a upper limit. falls to zero as the ball hits the land. so rises up once more to the following upper limit which will be less than the old 1. This moving ridge repeats until the ball comes to rest. This graph will ne’er be negative. since the ball ne’er falls below land degree. Almost everybody. at some point in their lives. has bounced a gum elastic ball against the wall or floor and observed its gesture. Normally we don’t believe about the inside informations of resiling ball natural philosophies excessively much as it’s reasonably obvious what is go oning — the ball fundamentally rebounds off a surface at a velocity proportional to how fast it is thrown. But what isn’t known to most is what is specifically go oning to the ball before. during. and after its brief impact with the surface.
To get down this account let’s foremost see what happens to a typical gum elastic ball that is dropped vertically onto a level horizontal surface. and which falls under the influence of gravitation.
In this account. the resiling ball natural philosophies will be broken down into seven distinguishable phases. in which the ball gesture ( before. during. and after impact ) is analyzed. To simplify the treatment let’s assume that the bounciness surface is difficult ( stiff ) . and that air opposition is negligible.
Let’s define the geometric centre of the ball as point C. the speed of point C as V. and the acceleration of point C as a. Let’s farther assume that the ball has unvarying denseness. which means that point C of the ball coincides with its centre of mass.
In this phase. the ball falls vertically downward under the influence of gravitation ( g ) . The speed V points downward. The acceleration a besides points downward. The magnitude of a is equal to g. in the absence of air opposition. ( Note that the acceleration due to gravitation is g = 9. 8 m/s2. on Earth ) . As shown in the above figure. the horizontal force F is the clash force moving on the ball due to reach with the surface. during impact. This force F is the cause of the speed and spin ( rotary motion ) reversal. This clash force is generated by the absorbing action of the ball with the surface. The way of this clash force is opposite the way of faux pas speed between ball and surface. during impact. Slip speed is the comparative horizontal velocity between the ball’s point of impact and the surface it is impacting.
Since this force F is moving to the right. it torques the ball counterclockwise. This causes the ball to alter its original spin way from clockwise Wisconsin to counterclockwise wF. after impact. This force besides causes the ball to speed up to the right during impact. This consequences in the horizontal speed constituent of the ball ( parallel to the surface ) to alter way and point towards the right. after impact.
In order for the ball speed and spin to change by reversal way it is necessary to hold a high coefficient of clash between ball and surface. This creates sufficient clash force F to be generated. which causes the spin and horizontal speed constituent of the ball to change by reversal way after impact with the surface.