Evaluate Magnitude of Gravitation at the Surface of a Planet

In summary, the question is asking for the magnitude of the gravitational field at the surface of a planet with no atmosphere, given a graph of the trajectory of a rock thrown from a height with an initial speed of 20.9 m/s. The initial launch angle can be approximated by drawing a tangent line to the curve at the start of the trajectory. Using the SUVAT equations, the x and y components of velocity can be found, along with the maximum distances traveled in the x and y directions. These values can then be used to solve for the time of flight and the launch angle, which can then be used to find the magnitude of the gravitational field. It is important to note that the given equation for x_max is not applicable
  • #1
ScrubTier
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1. The trajectory of a rock thrown from a height with an initial speed of 20.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.
https://s2.lite.msu.edu/cgi-bin/plot.png?file=muiblack_msu_1442688985_1543723_plot.data

Homework Equations



Tangent = Opposite/Adjacent
Xmax=Vo^2/a*sin2Theta=Vo^2/a*2sinTheta*cosTheta[/B]

The Attempt at a Solution



Rise = 15 Run=20
Tan(x)=15/20
x=36.869 I think. I got this number but plugging this back in is not working for me. I thought I would take this and plug it into a triangle where h=20.9 (Vo) then the y-component would be the answer. This is not working.[/B]
 
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  • #2
ScrubTier said:
1. The trajectory of a rock thrown from a height with an initial speed of 20.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.
https://s2.lite.msu.edu/cgi-bin/plot.png?file=muiblack_msu_1442688985_1543723_plot.data

Homework Equations



Tangent = Opposite/Adjacent
Xmax=Vo^2/a*sin2Theta=Vo^2/a*2sinTheta*cosTheta[/B]

The Attempt at a Solution



Rise = 15 Run=20
Tan(x)=15/20
x=36.869 I think. I got this number but plugging this back in is not working for me. I thought I would take this and plug it into a triangle where h=20.9 (Vo) then the y-component would be the answer. This is not working.[/B]
What is x supposed to be? What units does it have? What does "evaluate the magnitude of the gravitational field" mean to you?
 
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  • #3
x is supposed to be the angle at which the rock is first thrown. It would be degrees. The magnitude of the gravitational field would be the constant y-component wherever the rock is on the graph.
 
  • #4
ScrubTier said:
x is supposed to be the angle at which the rock is first thrown. It would be degrees. The magnitude of the gravitational field would be the constant y-component wherever the rock is on the graph.
No, I don't think so. According to the graph of the trajectory, there is no constant y-component. It keeps changing ...

Since this is a planet which is presumably not earth, I think the "magnitude of the gravitational field" means finding the value of g for this planet.
 
  • #5
But how would I do that then? I'm so lost.
 
  • #6
ScrubTier said:
But how would I do that then? I'm so lost.
Write out the equations for projectile motion under a constant gravitational acceleration. You'll use the information from the graph of the trajectory to help you solve for the value of g for this planet.
 
  • #7
Is it like the equation I included?
 
  • #8
ScrubTier said:
Is it like the equation I included?
No.
The usual SUVAT equations allow you to write out the horizontal and vertical displacements as functions of time. But your graph says nothing about time. It shows a trajectory, i.e. the relationship between x and y. If you have an equation showing how x depends on t, and another showing how y depends on t, how would you obtain an equation that shows how y depends on x?

That said, there is a way to use the equation you posted. First, you have to understand what exactly xmax refers to in that equation and read that off the graph. You also need to ead theta from the graph, but it will be hard to do that with any accuracy. So I recommend working with the SUVAT equations as I described above.
 
  • #9
Would I need Xmax and Ymax to use those equations? My professor said we should be able to read those from the graph but it isn't so clear..
 
  • #10
What I have figured out is that I can find the x-component of Velocity by my given velocity (20.9) times cos(Launch angle) and my y-component by 20.9*sin(launch angle) but how do I find the launch angle? Can I use an angle found on the downslope?
 
  • #11
ScrubTier said:
What I have figured out is that I can find the x-component of Velocity by my given velocity (20.9) times cos(Launch angle) and my y-component by 20.9*sin(launch angle) but how do I find the launch angle? Can I use an angle found on the downslope?
It's not clear what you mean by "downslope" here.

Since you are given a plot of its trajectory, you can find (or approximate) the angle which the projectile takes when it is launched.
 
  • #12
I don't understand how to do that.
 
  • #13
ScrubTier said:
I don't understand how to do that.
Well, take the sketch and try to draw a tangent to the curve at the start of the trajectory. The angle this tangent line makes to the horizontal will be launch angle, or a close approximation.
 
  • #14
I know how to find the angle I just don't know what measurements to use. Would x=0, 20 y=15, 30 be close enough?
 
  • #15
I just tried by using those numbers. It was wrong. I know I must use something to find the Launch Angle then find x-component of velocity and y-component of velocity. Then determine the Xmax (distance which it traveled when it made it back to the starting height (15m)) and Ymax (max height it got to). I use these in d(Xmax)=Vo(x)*t to find t then d (which is 0) = Vo(y)*t-1/2*g*t^2
I just do not know what numbers to use to find these things!
 
  • #16
ScrubTier said:
I just tried by using those numbers. It was wrong. I know I must use something to find the Launch Angle then find x-component of velocity and y-component of velocity. Then determine the Xmax (distance which it traveled when it made it back to the starting height (15m)) and Ymax (max height it got to). I use these in d(Xmax)=Vo(x)*t to find t then d (which is 0) = Vo(y)*t-1/2*g*t^2
I just do not know what numbers to use to find these things!
Well, we can't help you if you don't post your calculations. You may be making mistakes with your artihmetic
 
  • #17
If you look at the picture of the graph finding coordinates to do calculations with is very un-exact. That is my problem.
 
  • #18
ScrubTier said:
If you look at the picture of the graph finding coordinates to do calculations with is very un-exact. That is my problem.
Yes, I understand that.

But what are we to suggest to you in response to the statement, "I got it wrong"?
 
  • #19
I really want advice as to what numbers I should use for my equations. Estimates to what Xmax should be would be helpful.
 
  • #20
ScrubTier said:
I know how to find the angle I just don't know what measurements to use. Would x=0, 20 y=15, 30 be close enough?
That looks somewhat off to me. As I posted, I think that estimating the launch angle directly from the graph is a rather inaccurate way to proceed. You would be much better off picking a point on the trajectory that is clear (max height gain and x at that point) and finding the gravitational acceleration and angle which hit it.
 
  • #21
Reading points from a graph is easier and usually more accurate than trying to estimate a slope by eye, particularly when the axes have different scales. I've taken your figure, added some additional rulings to the axes to aid in estimating readings, and indicated a few points that you might find useful in working the problem:
Fig3.gif
 

1. What is the formula for calculating the magnitude of gravitation at the surface of a planet?

The formula for calculating the magnitude of gravitation at the surface of a planet is: F = (GmM)/r^2, where F is the force of gravity, G is the universal gravitational constant, m and M are the masses of the planet and object, and r is the distance between the center of the planet and the object.

2. How does the mass of a planet affect the magnitude of gravitation at its surface?

The greater the mass of a planet, the greater the magnitude of gravitation at its surface. This is because the force of gravity is directly proportional to the mass of both objects involved.

3. How does the distance from the center of a planet affect the magnitude of gravitation at its surface?

The closer an object is to the center of a planet, the greater the magnitude of gravitation at its surface. This is because the force of gravity is inversely proportional to the square of the distance between the two objects.

4. How is the magnitude of gravitation at the surface of a planet related to the planet's size?

The magnitude of gravitation at the surface of a planet is directly proportional to the planet's size. This means that as the size of the planet increases, the magnitude of gravitation at its surface also increases.

5. Why is it important to calculate the magnitude of gravitation at the surface of a planet?

Calculating the magnitude of gravitation at the surface of a planet is important for understanding the behavior of objects on the planet's surface. It also helps in predicting the motion of objects and understanding the gravitational interactions between planets and other celestial bodies.

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