What Does an Acceleration-Time Graph Look Like for an Inelastic Collision?

[thereddevils]

Homework Statement

A steel ball is dropped from a table and rebounds several time. Sketch the acceleration time graph if the collision is inelastic.

Homework Equations

The Attempt at a Solution

I am not really sure how to go about this.

 

[JaredJames]

You need to draw a per of axis where x = time and y = acceleration.

The acceleration of the steel ball is going from positive to negative. +9.8m/s^2 during the descent, -9.8m/s^2 during the ascent after the bounce. So the time goes from 0 to (time when it stops bouncing) and the acceleration goes from +9.8m/s^2 to -9.8m/s^2.

When the bar goes switches from above the x-axis to below it means the ball is changing direction (rising or falling).

Your axis should look roughly like this: http://sciencecity.oupchina.com.hk/npaw/student/glossary/acceleration_time_graph.htm and it also has an example of the bars to use.

You use blocks as the acceleration due to gravity being constant.

Your vertical height of the bar shows the acceleration due to gravity - your vertical height should always be +/- 9.8m/s^2.
Your horizontal width of the bar is the duration of the ascent / descent.

Your first bar (with positive acceleration of 9.8m/s as the ball is dropped) should be your widest and they will decay (get narrower) towards the right-hand side of the graph until eventually the ball stops bouncing - so there is no bar present.

Let me know if you require any more help,

Jared

 

[thereddevils]

You need to draw a per of axis where x = time and y = acceleration.

The acceleration of the steel ball is going from positive to negative. +9.8m/s^2 during the descent, -9.8m/s^2 during the ascent after the bounce. So the time goes from 0 to (time when it stops bouncing) and the acceleration goes from +9.8m/s^2 to -9.8m/s^2.

When the bar goes switches from above the x-axis to below it means the ball is changing direction (rising or falling).

Your axis should look roughly like this: http://sciencecity.oupchina.com.hk/npaw/student/glossary/acceleration_time_graph.htm and it also has an example of the bars to use.

You use blocks as the acceleration due to gravity being constant.

Your vertical height of the bar shows the acceleration due to gravity - your vertical height should always be +/- 9.8m/s^2.
Your horizontal width of the bar is the duration of the ascent / descent.

Your first bar (with positive acceleration of 9.8m/s as the ball is dropped) should be your widest and they will decay (get narrower) towards the right-hand side of the graph until eventually the ball stops bouncing - so there is no bar present.

Let me know if you require any more help,

Jared

Thanks Jared, you are so helpful! I have a few questions here, the graph you linked me to has only one bar. Wouldn't the shape of the graph look like a horizontal pyramid, where the first 2 bars are the maximums and the rest decreases in height as time passes?

 

[JaredJames]

Thanks Jared, you are so helpful! I have a few questions here, the graph you linked me to has only one bar. Wouldn't the shape of the graph look like a horizontal pyramid, where the first 2 bars are the maximums and the rest decreases in height as time passes?

The linked graph is an example, yours will have multiple bars, all the same height, but all with constantly diminishing widths. The first will be in the positive region, the second in the negative, the third in the positive and so on.

A pyramid instead of blocks would imply the acceleration is changing. This is not so. Acceleration due to gravity is constant and so a it is always 9.8m/s^2 during the balls ascent / descent. The height of the bars will not decrease as the acceleration is constant. The width however will, as the height of each bounce decreases the time the bounce takes will decrease and so the width of the bars will become less.

Everything I put in my first post stands.

The attachment to this post is an example of what your graph should look like.

Jared

 

[thereddevils]

The linked graph is an example, yours will have multiple bars, all the same height, but all with constantly diminishing widths. The first will be in the positive region, the second in the negative, the third in the positive and so on.

A pyramid instead of blocks would imply the acceleration is changing. This is not so. Acceleration due to gravity is constant and so a it is always 9.8m/s^2 during the balls ascent / descent. The height of the bars will not decrease as the acceleration is constant. The width however will, as the height of each bounce decreases the time the bounce takes will decrease and so the width of the bars will become less.

Everything I put in my first post stands.

The attachment to this post is an example of what your graph should look like.

Jared

Thanks again for enlightening me on this.