Lab Exercise: Measuring "g" using Conservation of Energy

In summary, the lab exercise involves measuring the acceleration due to gravity ("g") by applying the principle of conservation of energy. Students conduct experiments where they drop an object from a known height and measure the time it takes to reach the ground. By calculating the potential energy at the starting height and equating it to the kinetic energy at the point of impact, students derive a formula to determine "g". This hands-on approach reinforces the concept of energy conservation and its practical application in physics.
  • #1
Envy9268
7
0
Homework Statement
Apply conservation of energy to relate the PE of your glider at the release point to its KE at the photogate, then solve for g. This formula will be our estimated value g_est for each run. Write down your g_est formula below, use Theorem 2 to conver v_avg to the instantaneous speed at the midpoint of the photogate [v(t_mp)], then calculate a numerical value of g_est for your first run. If your g_est is off by 1 m/s^2 or more, carefully re-check and/or repeat your measurements before moving on to the next run.
Relevant Equations
KE = (1/2)mv^2
Theorem 1: v_avg = Δx/Δt = (v+v_0)/2
Theorem 2: v_avg = v(t_mp) (relating average velocity to instantaneous velocity at the midpoint in time)
Hi, so this is a lab in which we used an air track at an angle and a glider to gather some data through various trials, ultimately to calculate "g". L_glider = 10.15 cm
x (photogate activation point) = 547.5 mm or 54.75 cm
x_0 (release point) = 1800.0 mm or 180.00 cm
(Δx)_midpoint = | x - x_0 | + (L_glider / 2) = 130.33 cm
θ = 12.3°
Δh = 27.8 cm
g_est = (1 / 2h)v^2 (derived from conservation of energy)

Trial 1 data
(Δt)_avg = 0.044 s
V_avg = 2962 cm/s
g_est = 1600000 cm/s^2

The last two values of Trial one are what I'm confused about. The glider having moved an average of 29.62 cm/s seems quite fast and calculated g_est seems ludicrous. Is there something I'm misunderstanding? The glider was released from rest. I thought the value we'd get should be around 981 cm/s^2.
 
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  • #2
What events is (Δt)_avg the time difference between?
 
  • #3
The time it takes for the glider to reach the photogate
 
  • #4
Envy9268 said:
The time it takes for the glider to reach the photogate
I think you are misunderstanding what (Δt)_avg is.

How does the photogate work? Exactly what are you measuring with it?

For what it’s worth, I get ca 960 cm/s^2 using your values without changing any decimal places.
 
  • #5
That's good news at least. I'm not sure what I'm missing then.
 
  • #6
Envy9268 said:
That's good news at least. I'm not sure what I'm missing then.
You should try to figure out these questions:
Orodruin said:
How does the photogate work? Exactly what are you measuring with it?
 
  • #7
Hmm, so is (Δt)_avg the average time required for the glider to pass through the photogate from start to finish? That makes more sense, because the photogate couldn't know when the glider was released.
 
  • #8
Envy9268 said:
because the photogate couldn't know when the glider was released.
Exactly. The photogate measures the time it was blocked. So what is the ##\Delta x## corresponding to the measured ##\Delta t_{\rm avg}##?
 
  • #9
That makes sense. According to the lab handout, it says Δx is the object's (vector) displacement.
 
  • #10
Envy9268 said:
That makes sense. According to the lab handout, it says Δx is the object's (vector) displacement.
Yes, but what does this mean in this case (in terms of an actual value!). How much is the glider displaced in the measured time interval?
 
  • #11
Would that not be the length of the glider, 10.15 cm?
 
  • #12
It would. So what do you get for the estimated value of ##g##?
 
  • #13
I'm now getting 950 cm/s^2, slightly off from your calculation, but much much more realistic. I wonder where the discrepancy is now, but thank you so much for helping me understand.
 

FAQ: Lab Exercise: Measuring "g" using Conservation of Energy

What is the purpose of the lab exercise measuring "g" using conservation of energy?

The purpose of this lab exercise is to determine the acceleration due to gravity (g) by using the principle of conservation of energy. By measuring the potential and kinetic energy of an object in free fall, students can calculate the value of g based on the energy transformations that occur during the fall.

How do we measure the height from which the object is dropped?

The height can be measured using a ruler or a measuring tape. It is important to measure from the point of release to the ground level, ensuring that the measurement is taken vertically to maintain accuracy. Additionally, using a fixed reference point can help in obtaining consistent measurements.

What equipment is typically used in this lab exercise?

Typical equipment for this lab includes a drop weight (such as a small ball), a measuring tape or ruler, a stopwatch to measure the time of fall, and a data collection device (like a computer or calculator) for analyzing the results. Some setups may also include sensors to automatically record the height and time.

What calculations are involved in determining the value of "g"?

To calculate "g," students first measure the height (h) from which the object is dropped and the time (t) it takes to reach the ground. The potential energy at height h is given by PE = mgh, and the kinetic energy just before impact is KE = 0.5mv². By equating the potential energy to kinetic energy and solving for g, students can use the formula g = 2h/t², where v (velocity) is derived from the time of fall.

What are some common sources of error in this experiment?

Common sources of error include inaccurate height measurements, timing errors when measuring the fall time, air resistance affecting the object's fall, and human reaction time in starting and stopping the stopwatch. Ensuring that the drop is executed in a controlled environment can help minimize these errors.

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