Determine the period of the motion

In summary, the conversation discusses a homework problem involving a ball being dropped from a height of 4.00 m and making an elastic collision with the ground. The goal is to determine the period of motion, with the assumption that no mechanical energy is lost due to air resistance. One person attempts to solve the problem using a formula for calculating period, but is confused by the answer given in the book. The other person suggests using a kinematic equation to find the time it takes for the ball to reach the ground, which is half of the total period. This leads to a solution for the problem.
  • #1
aliciagu
7
0
Out of ideas, and frustrated!

Homework Statement


A ball dropped from a height of 4.00 m makes an elastic collision with the grond. Assume that no mechanical energy is lost due to air resistance. Determine the period of the motion


Homework Equations



I know the period (T) = the time required for the object to make one cycle.

The Attempt at a Solution



I get: 4m/9.8 m/s^2=.408 s^2 s=.639 (square root of .408) .639 x 2= 1.278 s (time for it to go down 4 m and up 4 m)
My book gives 1.81 s as the answer. I can get that if I take the square root of 8/9.8 (8 being the total distance traveled in one period) and multiply it by 2. But why? That would be the time required for 2 periods, wouldn't it? I'm banging my head againstthe wall on this one!
 
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  • #2
you can calculate the time for it to reach the ground from the kinematic eq:

y = 1/2 at^2. The time for this will be the way down, or 1/2 the cycle.
 
  • #3
That answers it! I knew I was missing something stupid!
 

1. What is the period of motion?

The period of motion is the amount of time it takes for an object to complete one full cycle of its motion.

2. How is the period of motion calculated?

The period of motion can be calculated by dividing the total time it takes for an object to complete one full cycle by the number of cycles completed.

3. What factors affect the period of motion?

The period of motion can be affected by the mass, speed, and length of the object's path. It can also be affected by external forces such as friction or air resistance.

4. What is the difference between period and frequency?

The period and frequency are inversely related. The period is the time it takes for one full cycle of motion, while frequency is the number of cycles completed in a given amount of time. Frequency is the inverse of the period, meaning that as the period decreases, the frequency increases.

5. How is the period of motion measured?

The period of motion can be measured using a stopwatch or timer to record the time it takes for an object to complete one full cycle of motion. Other measuring tools such as a pendulum or ruler can also be used to determine the period of motion.

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