Ball dropped, elastic collision, harmonic motion

In summary, the problem involves a ball dropped from 4m with a perfectly elastic collision with the ground. The goal is to show that the motion is periodic and determine the period of the motion. Using the equations yf-yi=vit+1/2ayt2 and a=-(w2)x, it was determined that the motion is periodic with a period of 2.86s. This was also confirmed by graphing the equation y=4-2.2t2. Additionally, the time to reach maximum extension was found to be 0.9s. However, there is some confusion regarding the time it takes for the ball to reach the ground, as the calculated time of 2.86s
  • #1
pb23me
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Homework Statement


A ball dropped from a height of 4m makes a perfectly elastic collision with the ground. Assuming that no energy is lost due to air resistance.
show the motion is periodic
determine the period of the motion



Homework Equations


yf-yi=vit+1/2ayt2
a=-(w2)x
a=9.8m/s2
mgyi+1/2mv2i=mgyf+1/2mv2f

The Attempt at a Solution

i first solved for w using a=-(w2)x and got w=2.2rad/s i then solved for T using T=2pi/w and got T=2.86s
i divided T by 4 to obtain t or time to max extension and got t=.9 sec
i also used the equation yf-yi=vit+1/2ayt2 and solved for t getting 2.86s? this is confusing because i set vi=0 yf=0 yi=4 and solved for t. I would expect that t be half of T since this would be the time from 4m to the ground.
 
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  • #2
I also showed that the motion is periodic by graphing the equation y=4-2.2t2 the period of the motion is 2.86s
 

1. What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the colliding objects is conserved. This means that the energy before the collision is equal to the energy after the collision. In an elastic collision, the objects bounce off each other without any loss of energy.

2. How does a ball dropped and a ball thrown horizontally differ in terms of elastic collision?

In a ball dropped scenario, the ball is only affected by the force of gravity, which causes it to accelerate towards the ground. In an elastic collision, the ball hits the ground and bounces back up with the same speed, as the energy is conserved. On the other hand, in a ball thrown horizontally, the ball has both a horizontal and vertical component to its motion. When it collides with the ground, the horizontal component remains constant, while the vertical component changes due to the force of gravity. This results in a curved path of motion.

3. What is harmonic motion?

Harmonic motion is a type of motion in which an object moves back and forth between two points, with a constant period and amplitude. This type of motion is often seen in springs, pendulums, and other oscillating systems.

4. How is harmonic motion related to elastic collision?

In elastic collisions, the colliding objects experience a change in momentum and direction. This change in momentum can be described as a type of harmonic motion, as the objects oscillate back and forth between two points (before and after the collision) with a constant period and amplitude.

5. Can a ball dropped from a certain height experience both elastic and inelastic collisions?

Yes, a ball dropped from a certain height can experience both elastic and inelastic collisions. If the ball hits a perfectly elastic surface, it will bounce back up with the same energy and speed. However, if the surface is not perfectly elastic, some of the energy will be lost during the collision, resulting in an inelastic collision. This means that the ball will not bounce back up with the same speed as before the collision.

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