Gravitational acceleration

In summary, the conversation revolves around a physics challenge given by a teacher. The challenge involves calculating the speed and time it takes for a rock to fall from 109 km above sea level to 34 km. The formulas given are the gravitational constant and the kinematics equations. The conversation covers different approaches to solving the problem, with one person suggesting using a chart with 0.5 second increments and another suggesting using calculus to account for the change in gravity. The conversation ends with a reference to a website that may provide further guidance on the problem.
  • #1
bticu
1
0
THIS IS NOT A HOME WORK, THIS IS JUST FOR FUN?

I've been given a challenge by my grade 11 physics teacher and I can't make heads of tail of it, I’ve got the formulas but the numbers don't make sense.
If you went up 109 km (above sea level) and dropped a rock, what speed would it be traveling at and how long would it take to reach 34 km (above sea level). Air resistance can be ignored.
Gravitational constant
=9.79 m/second*second
This is the only formulas he gave me.
Where do I even start?
Distance:
Distance to be traveled = 109km - 34km
Distance to be traveled = 75km
I then started making a chart going by 0.5 second increments
Example:
{Time} (Acceleration) [calulation]
{0.5 sec} (39.16m) [9.79/(0.5*0.5)]
{1 sec} (9.79) [9.79/(1*1)]
{1.5 sec} (4.35) [9.79/(1.5*1.5)]
{2 sec} (2.44) [9.79/(2*2)]
{2.5 sec} (1.57) [9.79/(2.5*2.5)]
{3 sec} (1.09) [9.79/(3*3)]
So could someone tell me is this is right
After 3 seconds, the rocks velocity is 58.4 M/S and traveled a distance of 156 meters
I got the distance by taking the time
{Time} (Acceleration) <Current speed> [calculation]
{0.5 sec} (39.16m) <39.16 m/s> [39.16]
{1 sec} (9.79) <48.95 m/s> [39.16+9.79]
{1.5 sec} (4.35) <53.30 m/s> [48.95+4.35]
{2 sec} (2.44) <55.75 m/s> [53.30+2.44]
{2.5 sec} (1.57) <57.32 m/s> [55.75+1.5]
{3 sec} (1.09) <58.40 m/s> [57.32+1.09]
I got my distance traveled by summing up my current speeds and deviding the total by 2 (2 samples per second speed is in meters per second)
My total speed is the total of my currentspeed
First thing is that correct?
Second thing is this is correct is there a better way of doing this?
If this is not correct, what is the correct calculation?
 
Last edited:
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  • #2
Just want to say before I begin that this might not be rite, and there is a good chance that the graphics won't come out quite how I want them to, but do your best with it.
I think that I can do part of it, so here goes...
First, we know that the following is true.
[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]
and
[tex]F = M_2a[/tex]
(Assuming that mass is constant)
Since air resistance can be ignored, you can work out the velocity from the change in gravitational potential to kinetic energy, so...
[tex] \frac{1}{2}M_2v^2 = \delta\frac{GM_1M_2}{r}[/tex]
So, rearrange for v and let r be the difference in radius from the centre of mass of the earth, so r includes the radius of the earth.
Now for the time. From the two equations before, we get
[tex]a = \frac{GM_1}{r^2}[/tex],
and using calculus, the following can be done...
[tex] dv/dt = \frac{GM_1}{r^2} [/tex]
So, t can be found by integration (Let one of the limits equal zero) since we know what v is. Note, that the value of the radius is in metres, and takes into account of the radius of the earth, as before.
Hope this is rite, and that it helps.:biggrin:
 
Last edited by a moderator:
  • #3
You might start by looking at

http://www.physicsclassroom.com/Class/1DKin/U1L5d.html

(or start at the beginning with)

http://www.physicsclassroom.com/Class/1DKin/U1L5a.html

If you are given the acceleration of gravity, it's likely your teacher intends you to believe its constant. More advanced calculations are possible which take into account the weakening of gravity as one gets further away from the Earth, but they require calculus to fully justify.
 
  • #4
have you learned the kinematics equations?
 

1. What is gravitational acceleration?

Gravitational acceleration, also known as acceleration due to gravity, is the acceleration experienced by an object when it is subjected to the force of gravity. It is the rate at which an object gains speed as it falls towards the Earth due to the Earth's gravitational pull.

2. How is gravitational acceleration calculated?

Gravitational acceleration can be calculated by dividing the force of gravity on an object by the mass of the object. The formula for gravitational acceleration is a = F/m, where a is the gravitational acceleration, F is the force of gravity, and m is the mass of the object.

3. Does gravitational acceleration change on different planets?

Yes, gravitational acceleration varies depending on the mass and size of the planet. The larger the planet, the stronger its gravitational pull, resulting in a higher gravitational acceleration. For example, the gravitational acceleration on Earth is 9.8 m/s², while on the moon it is only 1.6 m/s².

4. How does altitude affect gravitational acceleration?

As altitude increases, the distance between an object and the center of the Earth also increases. This results in a decrease in gravitational acceleration. This is why objects weigh less at higher altitudes compared to at sea level.

5. What is the significance of gravitational acceleration?

Gravitational acceleration plays a crucial role in understanding and explaining various phenomena, such as the motion of celestial bodies, the behavior of objects in free fall, and the formation of planets and stars. It also helps us understand the concept of weight and the effects of gravity on our daily lives.

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