Pre Lab Questions: Billiard Ball Collides Head-On With Bill ✓ Solved

Pre Lab Questions A Billiard Ball Collides Head On With Billiard Ball

Pre-Lab Questions · A billiard ball collides head-on with billiard ball at rest. · Sketch a position vs. time graph for each ball, include position before the collision, once the collision occurs and after the collision. · What can be said about the conservation of momentum for the collision? Explain your answer. · Write down the total momentum for two marbles of mass, m, both moving at velocity, v. What is the kinetic energy of the system? · When you drop two marbles at once, why doesn’t only one marble come off the end twice as fast? Write down the kinetic energy of one marble with mass m and velocity 2v and compare this to your answer in Experiment 1 Post Lab Question 4 to check. Note: Assume the collisions are perfectly elastic.

Experiment 1: Conservation of momentum Data Sheet

Table 1. Collision Data- Moving and Stationary Marbles

Number of Flicked Marbles, Number of Stationary Marbles, Number of Marbles that Leave the Runway

Table 2. Collision Data- Moving Marbles

Number of Marbles on Right Side of Runway, Number of Marbles on Left Side of Runway, Number of Marbles that Leave the Right Side of the Runway, Number of Marbles that Leave the Left Side of the Runway

Post-Lab Questions

· What kind of collision is exhibited by the marbles in this experiment and why?

· When one marble hits the end of the line of marbles, how many shoot off the other end? Describe the momentum of the set of marbles before and after the collision (assume elastic collisions).

· How did the speed of the marble that comes off the end of the line change as you increased the speed of the marble that travels down the chute? Use what you know about the conservation of momentum to describe what is happening.

· What happened when you sent two marbles down the runway? Is this what you predicted? Explain why or why not.

· How did the result change when both marbles were moving toward each other before the collision?

· What do you predict would happen to two marbles after a collision if you slowly rolled a marble down the runway and then flicked a second marble faster in the same direction?

Sample Paper For Above instruction

The principles of conservation of momentum and elastic collisions are fundamental to understanding the dynamics of colliding billiard balls and marbles. This experiment aims to investigate these concepts through a series of predicted and observed behaviors in controlled collisions, with a focus on highly elastic interactions where kinetic energy and momentum are conserved.

In the initial phase, a billiard ball at rest is struck head-on by a moving ball. Theoretical analysis suggests that the momentum before and after the collision remains constant, reflecting the law of conservation of momentum. To visualize this, a position versus time graph would illustrate the incident motion of both balls approaching the collision point, followed by the collision phase, and the post-collision trajectories. For the moving ball, the graph would show a decline in position over time until the collision, after which it would exhibit a reduced slope, indicating decreased velocity. Conversely, the stationary ball’s graph would remain flat until impact, then show an upward movement as it is set in motion, ideally with symmetrical velocity changes if the collision is perfectly elastic and symmetrical.

Mathematically, the total momentum of two marbles each of mass m and moving at velocity v is given as p = 2mv. The total kinetic energy before collision in an elastic interaction is KE = 1/2 mv^2 + 1/2 mv^2 = mv^2. When both marbles are dropped simultaneously, intuition might suggest that only one marble would move at twice the velocity, but because momentum is conserved across the system, both marbles share the energy transfer. For example, if one marble is hit with velocity v, the other could recoil with an equal velocity in the opposite direction, reflecting energy and momentum exchange consistent with elastic collisions.

The experimental observations align with predictions based on physics principles. When two marbles are struck simultaneously or sequentially, the set’s behavior demonstrates elastic collision characteristics: total system momentum remains constant, and kinetic energy is approximately conserved. In practice, slight deviations occur due to minor energy losses or experimental imperfections, but the overall trend confirms theoretical expectations.

Increasing the initial speed of a marble traveling down the chute results in a proportional increase in the speed of the marble exiting the collision. This supports the conservation of momentum, which stipulates that the total system momentum before impact equals the total after. When multiple marbles are involved—either moving in the same or opposite directions—the outcome depends on initial velocities and masses. Collisions between particles in motion exhibit predictable transfer of velocity and directionality, consistent with Newtonian mechanics.

The experiments predict that if a slow-moving marble is followed closely by a faster one in the same direction, the faster marble will transfer some of its momentum upon collision, causing the slower marble to accelerate slightly and the faster marble to decelerate correspondingly. Conversely, if two marbles approach each other, the collision results in a significant exchange of momentum, often causing the marbles to reverse directions or alter velocities drastically. Such behavior exemplifies elastic collision mechanics, where kinetic energy and momentum are redistributed among the colliding particles.

In conclusion, the experiments and their underlying physics principles demonstrate that elastic collisions conserve momentum and kinetic energy. Through close observation and measurement, one confirms that the behaviors of marbles and billiard balls in these interactions adhere to Newtonian mechanics, validating theoretical models. These findings have broad implications in understanding collision phenomena across various physical systems, from microscopic particles to macroscopic objects in motion.

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