# Particle in hemispherical bowl

• sailsinthesun
In summary, the problem involves a 195 g particle being released from rest at point A in a frictionless, hemispherical bowl with a radius of 31.0 cm. The task is to calculate the gravitational potential energy at point A relative to point B, the kinetic energy and speed at point B, the kinetic energy at point C, and the potential energy at point C. Using the equations PE=mgh and KE=.5mv^2, the potential energy at point A is found to be .59241J and the potential energy at point C is .39494J. The conservation of energy is used to find the kinetic energy at point B and the velocity at point C.
sailsinthesun
[SOLVED] Particle in hemispherical bowl

## Homework Statement

A 195 g particle is released from rest at point A along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 31.0 cm.
http://www.webassign.net/pse/p8-52.gif

(a) Calculate the gravitational potential energy of the particle-Earth system when the particle is at point A relative to point B.
(b) Calculate the kinetic energy of the particle at point B.
(c) Calculate its speed at point B.
(d) Calculate its kinetic energy when the particle is at point C.
(e) Calculate the potential energy when the particle is at point C.

## The Attempt at a Solution

(a)PE=mgh so PE=.195kg*9.8m/s^2*.31m=.59241J

(b)KE=.5mv^2 but I have no idea how to find the velocity at the point. Any help?

(d)Also need to know how to calculate velocity at this point...

(e)PE=mgh=(.195kg)(9.8m/s^2)(.2067m)=.39494

Any help on b, c, and d?

Hi sailsinthesun!

(a) and (e) seem ok.
sailsinthesun said:
(b)KE=.5mv^2 but I have no idea how to find the velocity at the point. Any help?

KE=.5mv^2 is the answer to (b)! That's all (b) asks you for!

For (c) and for (d), you use "conservation of energy": KE + PE = constant (which, btw, should be in your "Relevant equations").

sailsinthesun said:
(b)KE=.5mv^2 but I have no idea how to find the velocity at the point. Any help?

(d)Also need to know how to calculate velocity at this point...

B) At point B the PE is 0 and due to the conservation of energy KE is the same as the answer to A.

C) Now knowing what KE is work backwards with KE=.5mv^2 to find the velocity.

D) Also due to the conservation of energy, in A you found PE and since KE was 0 the entire energy of the system KE + PE = .59241J. So having the PE you found in part E you can substitute and find the KE.

## 1. What is a particle in a hemispherical bowl?

A particle in a hemispherical bowl is a common physics problem that involves a small object (the particle) rolling around the inside of a bowl that is shaped like half of a sphere.

## 2. What is the purpose of studying particles in hemispherical bowls?

Studying particles in hemispherical bowls can help us understand the dynamics of objects in curved surfaces and how they move under the influence of gravity and other forces. It is also a useful model for studying other systems, such as celestial bodies like planets and moons.

## 3. What variables affect the motion of a particle in a hemispherical bowl?

The motion of a particle in a hemispherical bowl is affected by several variables, including the mass of the particle, the shape and size of the bowl, the initial position and velocity of the particle, and any external forces acting on the particle, such as friction or gravity.

## 4. How is the path of the particle determined in a hemispherical bowl?

The path of the particle in a hemispherical bowl is determined by the interplay of the forces acting on the particle. The particle will follow a curved path due to the influence of gravity and the shape of the bowl, and this path can be calculated using mathematical equations and principles of physics.

## 5. Are there any real-world applications of studying particles in hemispherical bowls?

Yes, there are several real-world applications for understanding particles in hemispherical bowls. For example, this concept is used in designing roller coasters and other amusement park rides, as well as in understanding the motion of satellites and other objects in space. It can also be applied to industrial processes involving curved surfaces, such as the motion of particles in a ball mill.

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