What Is the Angle Where a Mass Leaves a Frictionless Sphere?

  • Thread starter Thread starter Newton's Protege
  • Start date Start date
AI Thread Summary
The problem involves determining the angle at which a mass leaves a frictionless sphere after sliding down. The solution requires understanding centripetal acceleration and conservation of energy principles, leading to the conclusion that the angle is 48 degrees. A mathematical proof can be succinctly presented in three lines. This problem is recognized as a classic textbook scenario, though it is not included in the user's textbook. Additional resources and discussions are available in related forum threads for further assistance.
Newton's Protege
Messages
2
Reaction score
0
My instructor has assigned me a bonus problem that I have no idea how to do. It is worth 25 points and I need these points very badly! I would be so grateful if anyone knows how to do this problem.

A mass sits on a frictionless sphere. The mass slides down the sphere to a certain point. The mass then acts like a projectile at that point. What is the angle of the point where the mass leaves the sphere. This angle is 48 degrees. Centripetalal acceleration is involved and so is conservation of energy. The instructor wants a mathematical proof of this. He said this can be accomplished within three lines on a sheet of paper. Apparenly, it is a classic "textbook problem" but it is absent from my textbook. I have enclosed an attached file to better illustrate what is happening
 

Attachments

Physics news on Phys.org
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 »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

I need opinions on a Projectile Motion problem that I made up
Replies
11
Views
2K
Work of gravity on an object sliding down a frictionless sphere
Replies
12
Views
2K
Velocity of particle leaving wedge
Replies
12
Views
2K
What Angle Causes a Mass to Leave a Frictionless Sphere?
Replies
13
Views
2K
Why is/is-not energy conserved in these scenarios?
Replies
14
Views
2K
Particle sliding down a sphere - When does it leave the sphere?
Replies
6
Views
3K
Conservation of Energy on a frictionless incline
Replies
2
Views
3K
Work and energy of an object on a ice slope
Replies
7
Views
1K
What Angle Does a Rice Grain Leave a Frictionless Billiard Ball?
Replies
4
Views
2K
Conservation of mechanical energy for skier on sphere
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top