Circular Motion and angle alpha

AI Thread Summary
The discussion revolves around calculating the angle alpha at which a plumb bob is deflected by the gravitational influence of a nearby mountain. The user attempts to derive a formula for alpha based on the mass of the mountain, the distance to its center, and the Earth's mass and radius, using gravitational force equations. They express uncertainty about their approach and seek clarification on estimating the mass of Mount Everest, suggesting it could be modeled as a pyramid or cone. The response emphasizes that a rough estimate is acceptable, encouraging the use of approximate values for dimensions and density. Overall, the conversation highlights the challenges of applying physics concepts to real-world scenarios, particularly in estimating parameters with limited information.
Carpe Mori
Messages
19
Reaction score
0

Homework Statement


A plumb bob is deflected from the vertical by an angle alpha due to a massive mountain nearby. (A) Find an approximate formula for alpha in terms of the mass of the mountain the distance to its center and the radius and mass of the earth
(B) Make a rough estimate of the mass of mt everest assuming it has the shape say of an equilateral pyramid or cone 4k m above its base and then (c) estimate the angle alpha of the pendulum bob if it is 5 km from the center of mt everest

Homework Equations



F= G*m1*m2/r^2

G = 6.67*10^-11

shoot idk throw some vector equations in there too

The Attempt at a Solution



well...i said
Mm = mass of mountain
m = mass of bob
Dm = Distance to mountain from bob
Fm = force exerted by mountain on bob
Me = Mass of earth
Re = radius of earth

Fm = G*Mm*m/(Dm)^2
g = G*Me/(Re)^2

i made a right triangle with vector mg, vector Fm and hypotnuse of the deflected bob string

using trig i got alpha = 90 - theta where tan(theta) = mg/Fm

I know this can't be anywhere near to right...and i don't want to attempt other parts before i get this...PLEASE HELP!
 
Last edited:
Physics news on Phys.org
That's right, if you really mean alpha=90-theta where tan(theta)=mg/Fm. Then tan(alpha)=Fm/mg.
 
Ok now can anyone help me figure out B...that is if i got A correct. I really honestly have no idea what they want me to do for B. Idk if I am supposed to look up values for this or what (i can find a rough volume of it i suppose but its not like i know the base or anything) I am certain there is NO more info on the question

PLZ HELP!
 
It says 'rough estimate'. This means 'order of magnitude'. You could say the base is a square 4km on a side, you could say it's a circle 3.5km in radius, it doesn't matter. They will only pay attention to the exponent in the angle (which will be REALLY small). You'll also need to know the density but you don't know the density either. Guess. Probably about the same density as any rock you can think of. Or the density of the earth, or even the density of water. You'll still be in the same ballpark.
 
well that problem was officially boring. Thank you very much Dick!
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Deviation of Plumb Bob In Uniform Circular Motion
Replies
11
Views
3K
Weight difference at Mt. Everest summit vs. sea level
Replies
2
Views
1K
Differential Equation for a Pendulum
Replies
21
Views
2K
Work done on a conical pendulum
Replies
3
Views
2K
How Does a Spring Impact the Angular Frequency of a Pendulum?
Replies
15
Views
6K
B Sign conventions in torque and non-uniform circular motion
Replies
1
Views
1K
Circular motion of a mass on a string on an inclined plane
Replies
14
Views
4K
Simulating a Rotary Inverted Pendulum in Python
Replies
15
Views
1K
I Lagrangian for pendulum
Replies
11
Views
2K
Calculating velocity needed for uniform circular motion?
Replies
19
Views
2K

Hot Threads

Recent Insights

Back
Top