Exploration 1: Understanding Conservation Laws
Observe the animation to see if you can discover any conservation laws. You should determine whether your laws hold for the left half of the animation, the right half of the animation, or the entire animation. Properties that you might want to consider are number of particles, color, and sum of the particle speeds. Restart.
The animation will run for \(100\) seconds.
Exploration 2: An Elastic Collision
The animation shows an elastic collision between two masses (position is given in centimeters and time is given in seconds). Restart.
- Set the initial velocity of the blue ball to zero. For the three conditions of the relative masses of the blue and red balls shown in the table, PREDICT what value (or values) of the initial velocity of the red ball will result in...
- both balls moving to the right after the collision.
- the red ball stopping after hitting the blue ball.
- the red ball moving to the left and the blue ball moving to the right after the collision.
| Enter the range of initial velocity values for the red ball that results in... |
...both balls moving to the right after the collision. |
...the red ball stopping after colliding with the blue ball. |
...the red ball moving to the left and the blue ball moving to the right after the collision. |
| \(m_{\text{red}} = m_{\text{blue}}\) |
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| \(m_{\text{red}} = 2\ast m_{\text{blue}}\) |
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| \(m_{\text{red}} = 0.5\ast m_{\text{blue}}\) |
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AFTER you have made your predictions, test them using the animation. Were you correct? If not, explain.
- Now set the initial velocity of the blue mass to \(-20\text{ cm/s}\), the initial velocity of the red mass to \(5\text{ cm/s}\), and the masses equal. PREDICT the direction each ball will be traveling after impact. AFTER you have made your prediction, try it. Were you correct? If not, explain.
- Set the initial velocity of the blue mass to \(-10\text{ cm/s}\) and the red mass to half the mass of the blue ball. PREDICT the velocity the red mass must have in order to completely stop the blue mass when they collide. Now try it. Were you correct? If not, explain.
- Set the initial velocity of the blue mass to \(-10\text{ cm/s}\) and the red mass to twice the mass of the blue ball. PREDICT the velocity the red mass must have in order to completely stop the blue mass when they collide. Now try it. Were you correct? If not, explain.
Exploration authored by Melissa Dancy.
Exploration 3: An Inelastic Collision with Unknown Masses
The initial velocities of the two carts in the animation can be changed by entering new values into the text fields (position is given in meters and time is given in seconds). As the carts approach one another they stick together. Restart.
Repeat the animation using varying velocities as you answer the following questions. Right-click on the graph to make a copy that can be expanded for better resolution.
- Run the animation using \(2\text{ m/s}\) and \(-2\text{ m/s}\) for the velocities of the left and right carts, respectively. What is the change in velocity of the left cart? The right cart? What is the ratio of these changes?
- Simulate collisions using other values of equal but opposite velocities. How does this effect the changes in the velocities? The ratio of the changes?
- Run the animation using \(1\text{ m/s}\) and \(-2\text{ m/s}\) for the velocities of the left and right carts, respectively. What is the change in velocity of the left cart? The right cart? What is the ratio of these changes?
- Is the ratio of the changes in the velocities always the same?
- What is the mass ratio of the carts?
Exploration 4: Elastic and Inelastic Collisions and \(\Delta p\)
Enter in a new value and click the "set values and play" button to register your values and run the animation (position is given in meters and time is given in seconds). We have set limits on the values you can choose:
\[0.5\text{ kg }<m_{1}<2\text{ kg},\quad 0\text{ m/s}<v_{1}<4\text{ m/s},\quad\text{and}\quad -4\text{ m/s}<v_{2}<0\text{ m/s}\nonumber\]
The bar graph gives an instantaneous reading of each cart's energy and the check box changes the collision type from perfectly elastic to perfectly inelastic. Restart.
Answer the following questions for both the elastic and inelastic collisions.
- Vary the mass and velocities. Is \(\Delta\mathbf{p}_{1}=-\Delta\mathbf{p}_{2}\)?
- Why should this be the case?
- Is the energy of the system constant? If not, where is it going?
Exploration 5: Two and Three Ball Collisions
If you drop a rubber ball and it hits the ground at \(5\text{ m/s}\), it bounces back at almost the same speed (position is given in meters and time is given in seconds). But what happens if you drop two balls stacked one upon another? A common lecture demonstration has a professor dropping a light ball and a heavy ball at the same time. The light ball is directly above the heavy ball so that the heavy ball hits the ground first, bounces back, and then hits the light ball which is still on its way down. Restart.
This animation uses two balls with a mass ratio of \(1:10\). We consider motion on a horizontal air track so we can ignore the effect of gravity so as to make the physics as clear as possible. The balls move at constant speed to the left before hitting the wall; assume all collisions are elastic.
- Predict the velocities of the balls after the first set of collisions, that is, when both balls are moving to the right.
- Predict the velocities if you use three balls with mass ratios of \(1:10:100\).
- Now run the animations. Were you correct? If not, explain why.
Note: The animation will run for \(100\) seconds.
Exploration 6: An Explosive Collision
The system's total kinetic energy is increased in a \(1200\text{-J}\) explosion in the animation (position is given in meters and time is given in seconds). Restart.
Use a mass ratio of \(1:2\) for the following questions.
- Draw energy diagrams for the system before and after the explosion.
- What percentage of the explosion's energy is converted to kinetic energy?
- What percentage of the explosion's energy is usable as kinetic energy?
- Is the process shown in the animation reversible?
Vary the mass of the left cart from \(0.1\text{ kg}\) to \(1.0\text{ kg}\) for the following questions.
- Does the larger or the smaller mass receive the most energy?
- Does the larger or the smaller mass receive the most momentum?
- Does the ratio of the two masses have any effect on the total resulting kinetic energy?
- Does the ratio of the two masses have any effect on the recoverable energy?
Exploration 7: A Bouncing Ball
The animation represents the seemingly simple example of a ball hitting the ground and bouncing back (position is given in meters and time is given in seconds). The graph can show velocity vs. time or acceleration vs. time and can be zoomed in to see the collision with the ground. Also shown are three bar graphs representing the different types of energy associated with the ball: the kinetic energy (orange), the gravitational potential energy (blue), and the elastic potential energy (green). Restart.
- There are three important time intervals during the animation. What are they? Briefly describe what is happening during these intervals.
- Draw energy diagrams, that is, find the values and plot a bar graph for the kinetic energy of the ball.
- Draw the graph of momentum vs. time. Describe what is happening to the momentum during the three important time intervals. If the momentum of the ball is changing, explain why.
- Draw the graph of the net force vs. time. Describe what is happening to the net force on the ball during the three important time intervals. If the net force of the ball is changing, explain why.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
