Finding the Acceleration of Gravity from these Dropped Ball Experiments

In summary, the conversation was about a lab where a ball was dropped and times were recorded to create three graphs. The confusion was around finding the values of g from the slopes of the height vs t^2 and sqrt of height vs t graphs. The individual tried using A=v/t to find velocity and then plugging into the equation, but got a large value for g. The conversation then shifted to discussing the equations used and determining the value of Yo as a function of t^2 to find g. It was also mentioned that dropping something from a higher height takes longer to reach the ground.
  • #1
Bobb
2
0
Homework Statement
Basically we did a lab where we dropped a ball and recorded the times then we created 3 graphs. Height vs t, height vs t^2. and sqrt of height vs. t. Where I'm confused is they want us to two 2 values of g from the slopes of the height vs t^2. and sqrt of height vs. t graphs. I thought the slope for height vs t^2 was already acceleration how would we find g from these?
Relevant Equations
X = Xo +Vot + 1/2at^2

0 = Yo + 0 -1/2gt^2
Did not know where to start so I tried A= v/t to find velocity then plug into equation to find g, but i got a huge g.
 
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  • #2
Bobb said:
Homework Statement: Basically we did a lab where we dropped a ball and recorded the times then we created 3 graphs. Height vs t, height vs t^2. and sqrt of height vs. t. Where I'm confused is they want us to two 2 values of g from the slopes of the height vs t^2. and sqrt of height vs. t graphs. I thought the slope for height vs t^2 was already acceleration how would we find g from these?
Homework Equations: X = Xo +Vot + 1/2at^2

0 = Yo + 0 -1/2gt^2

Did not know where to start so I tried A= v/t to find velocity then plug into equation to find g, but i got a huge g.
Let’s see your graph of height vs t^2
 
  • #3
Second one, teacher wanted it to be in y= mx+b form
 

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  • #4
Bobb said:
Second one, teacher wanted it to be in y= mx+b form
How can the height be increasing with time?
 
  • #5
Chestermiller said:
How can the height be increasing with time?
If you drop something from higher up it takes longer to get to the ground.

Bobb said:
0 = Yo + 0 -1/2gt^2

So what does this tell you about Yo as a function of t^2? If you let t^2 = s, you are asked to find g by computing the slope of the function Yo(s).
 
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  • #6
Orodruin said:
If you drop something from higher up it takes longer to get to the ground.
Ah. I was confused. I though he was measuring the distance fallen in a single drop as a function of time.
 

FAQ: Finding the Acceleration of Gravity from these Dropped Ball Experiments

What is the acceleration of gravity?

The acceleration of gravity, denoted as g, is the rate of change of velocity of an object due to the force of gravity. It is a constant value on Earth, approximately equal to 9.8 meters per second squared (m/s^2).

How can we measure the acceleration of gravity?

One way to measure the acceleration of gravity is by conducting experiments with dropped balls. By timing how long it takes for a ball to fall from a certain height and using the formula g = 2h/t^2, where h is the height and t is the time, we can calculate the acceleration of gravity.

Why is it important to find the acceleration of gravity?

Knowing the acceleration of gravity is important in many scientific fields, such as physics and engineering. It helps us understand the motion of objects and predict their behavior, as well as design structures and machines that can withstand the force of gravity.

What factors can affect the results of dropped ball experiments?

There are several factors that can affect the results of dropped ball experiments, including air resistance, the shape and size of the ball, and the precision of the timing device. It is important to control these variables as much as possible to get accurate results.

How can we improve the accuracy of our measurements in dropped ball experiments?

To improve the accuracy of our measurements, we can repeat the experiment multiple times and take an average of the results. We can also use a more precise timing device and minimize any external factors that may affect the experiment. Additionally, performing the experiment in a vacuum can eliminate the influence of air resistance.

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