# Measuring gravitational force of the Earth

• Ipos Manger
In summary, the conversation discusses different methods for measuring the gravitational force of the Earth using falling objects. The options mentioned include using a scale, a microphone, a free-fall apparatus, a digital camera, and an Atwood machine. The conversation also mentions the importance of averaging results and accounting for error in measurements. The use of a pendulum is suggested as a more accurate alternative to free-fall experiments. The conversation ends with a mention of using a spring and a video camera to measure the time of fall.
Ipos Manger
Hello, our teacher told us that how could we find the gravitational force of the Earth, and i wanted to do it with falling objects (Only option i got, no pendulums).
Does anyone have an idea what is a free-fall apparatus? I wanted to measure it just with a cronometer, but i need more precise results.. This homework is for Monday.
Any suggestions?
THANKS!

A scale ? :D
A scale is a device that indirectly measures forces.
But your teacher might not appreciate...

Well, I'm going to do it with falling objects, i need something that can record time with accuracy. And with scales.. You're measuring force directly. I need to relate the height of fall and the time taken.

A microphone ?
Then...

A microphone for what? o.o

Ever see Mythbusters? They routinely calculate the speed of objects, you could easily use distances and time to find acceleration.

So you're saying that i should use v2=2gs instead of s=gt2/2?

And how could i measure the final velocity?

no you can use the equation you plan to use, but utilize their apparatus and filming idea. You wouldn't be able to calculate an accurate final velocity for a given falling distance because it is changing, if you looked at a distance and a certain time to fall that distance, it would only be an average velocity.

maybe you could hold a stopwatch in the camera's view to incorporate a time reference with the positions as it falls

Right. But do you have any idea on how to do it with home-made materials? Or not too expensive?
Or could you give me the link of that Mythbusters video?
THANKS!

do you have a digital camera, they can usually take video. Then, think of a way to reference distance or position on the video, and think of a way to show what time the object was at each position. I will leave that up to you. Google Mythbusters if you need to see how they do it. I don't want to completely do your homework for you.

Alright calm down lol. I was just asking.

So you mean that i should record when the object falsl and then stop it when it touches the ground?

Yea, I suppose the simplest method would be to just find the time from drop to hitting ground from a known height. Then y=1/2 gt$^{2}$, and you would know t and y so you can solve for g. I just noticed that you need to find the gravitational force, not acceleration. Do you know how to find that if you know g?

Yeah, i wanted to measure g (Sorry if you're getting confused, English isn't my main language).
Do you know about the "free-fall" apparatus?

I just googled it... Essentially it is just a way to measure the time an object takes to fall a certain distance. But you just need to use some drop height, whatever you want. Maybe the height of your arm straight out, or from you standing on a chair, whatever. Then you need to measure the time using the most precise instrument you can get, like a stopwatch. Just run several trials and average out your results. Is that what you are looking to do?

Yeah, i was planning on dropping the ball at height 0.7m,0.8m,0.9m and 1m.
That way the height is easily calculated, but the main problem is the time taken...

Yea, that works, then just use a stopwatch or a digital watch (with seconds, or better yet with thousandths of seconds). Using different heights works, but do several trials for each height. If, you don't clock the time correctly for only one trial it will give you the wrong answer, but if you do, say, 5 trials and average out the g's then it accounts for the error of how you are measuring time, and helps to negate the error. But, it is also important for you to report what could have caused errors in your measurements and understand how that could affect your results.

Alright thanks. I'll try that and tell you if it works!
Just in case, how does a free fall apparatus work?

Fancy ones in a school lab use a sensor hooked up to a computer to get an accurate time and then you measure the distance of the fall.

You can easily make a pendulum out of a heavy object and some string. I had students do this as part of my student teaching (as well as the freefall) but the pendulum produced more accurate results.

Well my teacher said no pendulums.. That's the problem lol.

If you can do anything but pendulums then you still have options besides timing a free-fall of a body. You could construct an Atwood machine (masses, strings, pulleys) to 'moderate' the acceleration to an easily timed value. In a similar fashion, you could slide (or roll) an object down a gentle slope to do the same. Both will involve doing a little mathematical work to relate the observed values to g; either take into account rotational and friction effects or make them negligible with respect to the other forces involved.

A ball bearing rolling down a smooth, gentle slope is an inviting concept...

And how could i measure g with the Atwood machine?

The equation should be:

a = g(m-m2)/(m+m2)

Ipos Manger said:
And how could i measure g with the Atwood machine?

The equation should be:

a = g(m-m2)/(m+m2)

When an object is allowed to free-fall you have a = g. Finding g means timing the fall of the object. The same applies with the Atwood setup, only here you can manipulate the acceleration rate to be an easily calculated fraction of g. A slower fall may make it easier to time accurately.

Alright.. seems to complicated, thanks anyways!

I've heard also of an experiment with a spring, how does it work?

Suspend the object with fishing line, set up a video camera, put a chronometer in the view of the camera, then cut the line? You don't have to start timing at the same time the object falls, just find the time difference.

## 1. How is the gravitational force of the Earth measured?

The gravitational force of the Earth is measured using a tool called a gravimeter. This device measures the acceleration due to gravity at a particular location on Earth.

## 2. What is the standard unit of measurement for gravitational force?

The standard unit of measurement for gravitational force is the Newton (N). This unit is equivalent to 1 kilogram-meter per second squared (kg·m/s²).

## 3. How does the mass and distance of an object affect the gravitational force?

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that as the mass of an object increases, the gravitational force also increases. Similarly, as the distance between two objects increases, the gravitational force decreases.

## 4. Can the gravitational force of the Earth change?

Yes, the gravitational force of the Earth can change. It can be affected by factors such as changes in the Earth's mass or changes in the distance between the Earth and other celestial bodies.

## 5. What is the difference between weight and gravitational force?

Weight is a measure of the force of gravity acting on an object, while gravitational force is the actual force of attraction between two objects due to their masses. Weight also takes into account the acceleration due to gravity at a particular location, while gravitational force is a constant value between two objects regardless of their location.

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