Measuring acceleration of gravity

[Lynxarin]

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

 

[TDgen47@IB]

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

[Florian Schwarb]

Hi,

 

What we did could be useful to you as well. You could simply knot a string in equal distances and then attach to each knot a screw-nut. By letting it fall down and recording the sound the screw-nuts make when falling to the ground, you can measure the time taken of the different screw-nuts to reach the ground. I suggest you take 5 screw-nuts and do at least 5 repeats in order to obtain sufficient data. The distance from each screw-nut to the ground would then be the independent variable and the time taken the dependent variable. By using s=vi*t + 0.5*a*t^2 (vi=initial velocity --> in our case 0, a=acceleration --> in our case the acceleration due to gravity, t=time taken to reach the ground, s=distance travelled to reach the ground) you can simply solve this equation for a(=g)=2*s/(t^2). 

[Vioh]

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

[maturk]

A very easy method for calculating the acceleration of gravity is by using a pendulum. I'm not sure if this is the most "exact" method because the accuracy of the result mainly depends on how well you conduct the experiment yourself. The equation for the period of a pendulum is the following:

 

 

As you can see, there are three variables in the equation and two constants. The variable that you are solving for is g, which simply means that you will have to measure T (period) and L (length of the pendulum). I'd recommend making a long pendulum, perhaps a metre or more long for this will make more precise calculations, and timing how long it takes for your pendulum to go back and forth (1 period) ten times. 

 

So lets say hypothetically that you have a pendulum of length 0.85 metres and you took the time that the pendulum took to make 10 oscillations to be 18.7 seconds. This means that your g will be = (4*pi^2*0.85m)/(18.7/10)^2 = 9.6 ms^-2. Notice that I divided 18.7 by 10 because this will give you the time required to make one oscillation. 

 

You could possibly repeat this experiment three times and perhaps even use different lengths to measure g. This doesn't take too long, approximately 20 minutes, and doesn't require any fancy equipment. All you need is some string, a small weight that you attach to the end of the string, and a stopwatch. 

 

Good luck!

[Lynxarin]

 

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

 

I'm not sure but I don not think we have a ticker-timer in our school. But I can check that with my teacher tomorrow. Thanks for the idea !

[Lynxarin]

A very easy method for calculating the acceleration of gravity is by using a pendulum. I'm not sure if this is the most "exact" method because the accuracy of the result mainly depends on how well you conduct the experiment yourself. The equation for the period of a pendulum is the following:

 

 

As you can see, there are three variables in the equation and two constants. The variable that you are solving for is g, which simply means that you will have to measure T (period) and L (length of the pendulum). I'd recommend making a long pendulum, perhaps a metre or more long for this will make more precise calculations, and timing how long it takes for your pendulum to go back and forth (1 period) ten times. 

 

So lets say hypothetically that you have a pendulum of length 0.85 metres and you took the time that the pendulum took to make 10 oscillations to be 18.7 seconds. This means that your g will be = (4*pi^2*0.85m)/(18.7/10)^2 = 9.6 ms^-2. Notice that I divided 18.7 by 10 because this will give you the time required to make one oscillation. 

 

You could possibly repeat this experiment three times and perhaps even use different lengths to measure g. This doesn't take too long, approximately 20 minutes, and doesn't require any fancy equipment. All you need is some string, a small weight that you attach to the end of the string, and a stopwatch. 

 

Good luck!

When we got this task our teacher had a special twist to it that I did not mention here, we would have to use our smartphones in some creative way, and your idea is really interesting because I had first planned to drop my phone and have some cushion or something for it to land on but that would just be a bit complicated to measure the time for when it lands as it is quite heavy and little air resistance. But now I realised that I could use my phone as a pendulum and use the charging cable as my string.

 

Thanks for the idea!

[TDgen47@IB]

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

So if I just place a body of mass 1kg on a weighing scale, the scale should read 9.8 newtons if the gravity is 9.8m/s^2...right?? So can't you just measure it this way? Also could you please explain in detail (with an example if possible because I can grasp better with examples) as to why my method would be wrong. I kind of get the idea that it would be wrong but I just want a clearer and detailed explanation, if that's not to much trouble. Sorry if I am misleading anyone but I'm just interested in learning. Thank you.

[maturk]

 

 

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

So if I just place a body of mass 1kg on a weighing scale, the scale should read 9.8 newtons if the gravity is 9.8m/s^2...right?? So can't you just measure it this way? Also could you please explain in detail (with an example if possible because I can grasp better with examples) as to why my method would be wrong. I kind of get the idea that it would be wrong but I just want a clearer and detailed explanation, if that's not to much trouble. Sorry if I am misleading anyone but I'm just interested in learning. Thank you.

 

 

Hello,

 

What sort of scale are you referring to? At least to my knowledge no scale except a spring scale (and these are highly inaccurate) record in Newtons. All of the scales that I have encountered only record mass, not weight, in units grams or kilograms. 

[TDgen47@IB]

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

So if I just place a body of mass 1kg on a weighing scale, the scale should read 9.8 newtons if the gravity is 9.8m/s^2...right?? So can't you just measure it this way? Also could you please explain in detail (with an example if possible because I can grasp better with examples) as to why my method would be wrong. I kind of get the idea that it would be wrong but I just want a clearer and detailed explanation, if that's not to much trouble. Sorry if I am misleading anyone but I'm just interested in learning. Thank you.

 

Hello,

 

What sort of scale are you referring to? At least to my knowledge no scale except a spring scale (and these are highly inaccurate) record in Newtons. All of the scales that I have encountered only record mass, not weight, in units grams or kilograms.

Well, yea I know that these are inaccurate, I had mentioned earlier that my method is not the most accurate one but just the one I could come up with at that moment...so forgive me if I causes any misunderstanding.

[maturk]

 

 

 

 

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

So if I just place a body of mass 1kg on a weighing scale, the scale should read 9.8 newtons if the gravity is 9.8m/s^2...right?? So can't you just measure it this way? Also could you please explain in detail (with an example if possible because I can grasp better with examples) as to why my method would be wrong. I kind of get the idea that it would be wrong but I just want a clearer and detailed explanation, if that's not to much trouble. Sorry if I am misleading anyone but I'm just interested in learning. Thank you.

 

Hello,

 

What sort of scale are you referring to? At least to my knowledge no scale except a spring scale (and these are highly inaccurate) record in Newtons. All of the scales that I have encountered only record mass, not weight, in units grams or kilograms.

Well, yea I know that these are inaccurate, I had mentioned earlier that my method is not the most accurate one but just the one I could come up with at that moment...so forgive me if I causes any misunderstanding.

 

That is okay! Don't worry about it I'll try to explain a little now. Think of it like this, the acceleration of gravity that you are quoting, that is 9.8ms^-2, is only an average figure (different locations feel a different force of acceleration) and it does not hold true if I was standing on top of Mount Everest or if I was high above the stratosphere in a jet. This is due to the inverse square property of distance and gravity expressed in the following equation:

 

g = GM/R^2

 

Now lets say that we do have a spring scale (shown in the image below) that records both masses and newtons and we are located on the surface of the earth where we know precisely that the acceleration due to gravity here is 9.8 ms^-2. Hence, if I weigh a 1kg object the spring scale will say that it is also 9.8 N. Now lets transport ourselves to a distance of 10000 km away from the surface of the earth so that we are literally in space now. Here, according to the equation above the acceleration due to gravity is approximately 1.5 ms^-2. Hence it would record that, in Newtons, that the 1 kg object weighs 1.5 N. However if you look at the picture below (a picture of an ordinary spring scale), 1.5 N corresponds with about 0.15 kg. Now you can probably see what the problem is. The scale says that the 1kg object actually weighs 0.15 kg now! This is because the scale that we use assumes that the acceleration of gravity is always 9.8 ms^-2 which is not true. Hence, Lynxarin can not just assume that a scale knows precisely that the acceleration of gravity in his school  is 9.8 ms^-2 because it it might be more or less. So, he must find some other way to record the acceleration of gravity without the use of a scale because the scale is probably calibrated so that it uses the average figure.  Hope I helped to make you understand this a bit more Cheers!

 

[TDgen47@IB]

Hi, What is the most exact method to measure the acceleration of gravity?

 

Keep in mind that I'm in IB1 so the method should be understandable and possible to carry out as a lab with the knowledge I have. 

 

Thanks, Daniel

 

The way that our class did the experiment was to use a ticker timer. We can connect one end of the ticker-tape to a small weight, and the other end to the ticker-timer. Then we can drop the weight to the ground. For every second, the ticker-timer will make a tick (a dot) on the tape, thus can help us record the position of the weight as it falls down.

 

Once you've got the position-time graph, then the rest is easy. You can calculate the velocity of the weight by taking the difference in position divided by difference in time. For example, suppose that at time t = 0.05s, the position is 0.03m; and at time t = 0.15s, the position is 0.17m; then the velocity at time t = 0.10s is . You can repeat this calculation for every time interval, thus you will be able to obtain the velocity-time graph (which we would expect to be a linear graph). Of course, this is not very accurate compared to the technique of calculus, but it's good enough.

 

Now, by using linear regression to find the slope of the velocity-time graph, you can easily figure out the acceleration due to gravity.

 

 

I am not in IB yet. But I do have an idea. I'm not sure if it's the most practical and accurate one but here goes:

Take a body having a mass of 1kg. Drop it from a height of 1metre onto a weighing machine. If the acceleration due to gravity is 9.8m/s^2, the weighing scale should read 9.8 newton.

 

Well, the experiment that you suggest won't work. If you drop something from height, the object will gain velocity (i.e. kinetic energy), thus the scale will have to push harder on the object to make it stop. In reality, the reading on the scale can show something above or below 9.8 N, depending on change in impulse and time of impact. But generally, it definitely won't be 9.8 N. Similar, if you jump from 1-meter height onto a weighing machine, then the scale won't show your exact weight, but only the force necessary to stop you from falling.

So if I just place a body of mass 1kg on a weighing scale, the scale should read 9.8 newtons if the gravity is 9.8m/s^2...right?? So can't you just measure it this way? Also could you please explain in detail (with an example if possible because I can grasp better with examples) as to why my method would be wrong. I kind of get the idea that it would be wrong but I just want a clearer and detailed explanation, if that's not to much trouble. Sorry if I am misleading anyone but I'm just interested in learning. Thank you.

 

Hello,

 

What sort of scale are you referring to? At least to my knowledge no scale except a spring scale (and these are highly inaccurate) record in Newtons. All of the scales that I have encountered only record mass, not weight, in units grams or kilograms.

Well, yea I know that these are inaccurate, I had mentioned earlier that my method is not the most accurate one but just the one I could come up with at that moment...so forgive me if I causes any misunderstanding.

That is okay! Don't worry about it I'll try to explain a little now. Think of it like this, the acceleration of gravity that you are quoting, that is 9.8ms^-2, is only an average figure (different locations feel a different force of acceleration) and it does not hold true if I was standing on top of Mount Everest or if I was high above the stratosphere in a jet. This is due to the inverse square property of distance and gravity expressed in the following equation:

 

g = GM/R^2

 

Now lets say that we do have a spring scale (shown in the image below) that records both masses and newtons and we are located on the surface of the earth where we know precisely that the acceleration due to gravity here is 9.8 ms^-2. Hence, if I weigh a 1kg object the spring scale will say that it is also 9.8 N. Now lets transport ourselves to a distance of 10000 km away from the surface of the earth so that we are literally in space now. Here, according to the equation above the acceleration due to gravity is approximately 1.5 ms^-2. Hence it would record that, in Newtons, that the 1 kg object weighs 1.5 N. However if you look at the picture below (a picture of an ordinary spring scale), 1.5 N corresponds with about 0.15 kg. Now you can probably see what the problem is. The scale says that the 1kg object actually weighs 0.15 kg now! This is because the scale that we use assumes that the acceleration of gravity is always 9.8 ms^-2 which is not true. Hence, Lynxarin can not just assume that a scale knows precisely that the acceleration of gravity in his school  is 9.8 ms^-2 because it it might be more or less. So, he must find some other way to record the acceleration of gravity without the use of a scale because the scale is probably calibrated so that it uses the average figure.  Hope I helped to make you understand this a bit more Cheers!

 

Thanks a lot mate!! That did help! Yea I can now see the problem with my idea. Thanks to lynxarin for posting this problem. Helped me revise and get my concepts straight.