Motion in one demansion, photogate timer problem

In summary, the experimental magnitude of freefall acceleration is given by g_{exp}=2\Delta{y}/{(\Delta{t}})^2.
  • #1
machinarium
12
0
Please help me quick everyone, thank you in advance.

Homework Statement


http://imgkk.com/i/EasJ1d.jpg
a/We have two photogates placed as in the figure. We drop a marble through these at a negligble distance above the upper gate. The upper starts a timer as the ball passes through its beam and the second stop the timer.
Prove that the experimental magnitude of freefall acceleration is given by
[tex]g_{exp}=2\Delta{y}/{(\Delta{t}})^2[/tex]
b/ For the setup and assume that gexp =9.81m/s2, what value of [tex]\Delta{t}[/tex] would you expect to measure.
c/This time, the upper photogate is placed 0.50cm lower than the first time. But we still drop the marble from the same height as the first time.
What value of gexp at this time will you determine?

Homework Equations

[tex]a = \frac{{\Delta v}}{{\Delta t}} = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}[/tex]

The Attempt at a Solution



Based on the problem, I think that [tex]\delta{t}[/tex] is the time when the marble passes through between two gates. But if it were, I couldn't get [tex]g_{exp}=2\Delta{y}/{(\Delta{t}})^2[/tex].
If it were not, I could do like that
We have [tex]{g_{\exp }} = \frac{{\Delta v}}{{\Delta t}}[/tex]
Because v0=0,
Hence,
[tex]g_{exp}=2\Delta{y}/{(\Delta{t}})^2[/tex]
 
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  • #2
For part a, the [itex]g_{exp}[/itex] is your free fall acceleration.

In order to prove it, start with these equations:
[tex]a=\frac{v_{2}-v_{1}}{t_{2}-t_{1}}[/tex]
as you have already written. But, also use this:
[tex]v_{avg}=\frac{\Delta y}{\Delta t}[/tex]
and rewrite it like this:
[tex]\frac{v_{1}+v_{2}}{2}=\frac{\Delta y}{\Delta t}[/tex]

In the second equation the Vavg is just the normal equation for "average" velocity, so you can rewrite it as the third equation, simply adding the two velocities (final and initial) and dividing by two (averaging them).

So use the first and third equations, to solve for "a", but remember in this case "a" IS g_exp. A little algebra is required, you can eliminate v1 because it starts from rest (v1=0).

Also you are correct, delta(t) is the time it takes to pass through the two gates. But I don't see why you say you couldn't solve for delta(t) from this:
[tex]g_{exp}=2\Delta y/(\Delta t)^{2}[/tex]
Because the only unknown in that equation is delta(t) which is what you want. The problem gives you g_exp, and delta(y) is just the distance between the two gates.

For c, you will have to redetermine the equation for g_exp because you will now have an initial velocity. Originally the ball was assumed to have an initial velocity of zero, but now that the top gate is lower, the ball will obtain some downward motion by the time it reaches the upper gate.
 
  • #3
Thank you too much Oddbio.
And I want too say more clearly about part c. That is the upper gate is placed accidentaly lower than before. So the problem ask us to calculate in that accident.
(This is problem 113, chapter 2 - Motion in one dimension - Physics for Scientist and Engineers 6th edtion - Tipler Mosca - Univer of Washington)
Here is my solution, is this correct, is there something need to be corrected?
http://imgkk.com/i/5Be70O.jpg
 
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  • #4
Yes they all look correct to me. Good job :)
 

1. What is motion in one dimension?

Motion in one dimension refers to the movement of an object along a single axis or direction. It is typically represented by a straight line graph, with the object's position changing over time.

2. What is a photogate timer?

A photogate timer is a device used to measure the time it takes for an object to pass through a beam of light. It consists of a light emitter and a sensor, and can accurately measure the time interval between when an object interrupts the beam of light.

3. What is the problem with using a photogate timer for motion in one dimension experiments?

The main problem with using a photogate timer for motion in one dimension experiments is that it assumes the object is moving in a straight line. If the object deviates from this path, the data collected may be inaccurate.

4. How can the photogate timer problem be addressed?

To address the photogate timer problem, it is important to ensure that the object being studied is moving in a straight line. This can be achieved by using a guide or track to restrict the object's movement to one dimension.

5. What are some possible sources of error when using a photogate timer in motion in one dimension experiments?

Some possible sources of error when using a photogate timer in motion in one dimension experiments include friction, air resistance, and human error in starting and stopping the timer. It is important to carefully control these variables and repeat the experiment multiple times to reduce the effects of error.

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