# Physics

posted by Shenaya

A hemisphere of radius r is placed on a horizontal plane and a small mass of "m" is placed on the top of the hemisphere.
Find the height from the ground to the mass m,at the moment it loses it's contact with the hemisphere.And the contact is frictionless.

If we take the speed of the mass m, at the top of the hemisphere, v,the forces acting on the mass in that moment are mg,R and the centripetal force.

And the moment the mass loses its contact with the hemisphere,the forces acting on it are R and mg,and the centripetal force(which is zero as the speed is zero.)(because for the mass to lose its contact with the hemisphere, the speed should be zero as R≠0)

Hope my thoughts are correct and please correct me if they are wrong!

So do we have to solve this applying the law of conservation of energy? But how do find the speed v at the top as both R and v are unknowns.We can't simply equate R and mg because of the centripetal force acting on the mass in that moment!

Any help would be appreciated! Thank you!

1. Shenaya

And in both cases R cannot be the same too.

2. MathMate

Try reaction=centripetal force,
mg(cos(θ))=mv^2/R
Yes, v^2 (at the time it leaves sphere) can be calculated using energy considerations.

3. Shenaya

But at the top if we apply F=ma towards the center of the hemisphere it would be,
mg-R=mv^2/r right? So how do we eliminate R?

4. MathMate

You don't have to worry about the top, just assume that it was off balance by some random motion, and acceleration will start from there where KE=0, and PE=mg(R) if we take reference elevation at the centre of the sphere. Then at at certain θ<pi/2, mg(cos(θ))=mv^2/R
PE=mgR(1-cos(θ)=mv^2/2=KE
The R will cancel out when you substitute.

## Similar Questions

1. ### dynamics

Find the mass center of a cylinder with height L and a hemisphere glued to the top with radius R. L=2R. The cylinder is standing up on its bottom end with hemisphere on top. Im so lost on this and cant use the formula to work.
2. ### Calc

A hemisphere of radius 5 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the …
3. ### Calculus

let a hemisphere of radium 5 be cut by a plane parallel to the base of the hemisphere thus forming a segment of height 2. find its volume using cylindrical shells... thanks
4. ### Calculus 2 / Physics

An underground tank full of water has the following shape 1) hemisphere of radius 5 m at the bottom 2) a cylinder of radius 5 m and height 10 m in the middle 3) a circular cone with base radius 5 and height 4 m at the top The top of …
5. ### physics

Consider two frictionless inclined planes with the same vertical height. Plane 1 makes an angle of 25.0 degree with the horizontal, and plane 2 makes an angle of 55.0 degree with the horizontal. Mass m_1 is placed at the top of plane …
6. ### Physics

A particle is at rest at the apex A of a smooth fixed hemisphere whose base is horizontal. The hemisphere has centre O and radius a. The particle is then displaced very slightly from rest and moves on the surface of the hemisphere. …
7. ### Math

A hemisphere of radius 7 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the …
8. ### Physics

A block of mass 77.0kg is placed at the top of a frictionless plane that is inclined 46 degrees to the horizontal. The height of the plane is 23.0 meters. Find the speed of the block at the bottom of the plane. Please show all your …
9. ### Physics

A block of mass 77.0kg is placed at the top of a frictionless plane that is inclined 46degrees to the horizontal. The height of the plane is 23.0meters. Find the speed of the block and the bottom of the plane. The correct answer is: …
10. ### physics

A block of ice of mass m rests on the very top of a smooth metal hemishpere. The tiniest nudge sends it sliding down the side of the hemisphere. The acceleration of gravity is g and the radius of the hemisphere is R. At what angle, …

More Similar Questions