Kinetic Energy of a Particle in a semi-spherical bowl

• Joshua Lee
In summary, kinetic energy is the energy an object possesses due to its motion. A semi-spherical bowl is a bowl with a shape that is half of a sphere, with a curved bottom and a circular opening on top. The kinetic energy of a particle in a semi-spherical bowl differs from that of a flat surface due to the changing gravitational force as it moves towards the center. This can be calculated using the formula KE = 1/2 * mv^2. Factors that can affect the kinetic energy in a semi-spherical bowl include the mass and velocity of the particle, the shape and depth of the bowl, and the force of gravity.
Joshua Lee

Homework Statement

A 410 g particle in a semi-spherical bowl of radius 0.9 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2.6 m/s. The acceleration of gravity is 9.8 m/s 2 . What is its kinetic energy at B? Answer in units of J.

KE= (1/2)mv^2

The Attempt at a Solution

KE= (1/2)(410)(2.6)^2= 1385.8

You should work with units, that would have helped you to spot your mistake here.

Remember that a joule is equal to 1 N⋅m

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

2. What is a semi-spherical bowl?

A semi-spherical bowl is a bowl with a shape that is half of a sphere, with a curved bottom and a circular opening on top.

3. How does the kinetic energy of a particle in a semi-spherical bowl differ from that of a flat surface?

In a semi-spherical bowl, the particle is subject to a changing gravitational force as it moves towards the center, resulting in changes in its kinetic energy. This is not the case on a flat surface where the gravitational force remains constant.

4. How is kinetic energy calculated in a semi-spherical bowl?

The kinetic energy of a particle in a semi-spherical bowl can be calculated using the formula KE = 1/2 * mv^2, where m is the mass of the particle and v is its velocity at a given point in the bowl.

5. What factors can affect the kinetic energy of a particle in a semi-spherical bowl?

The kinetic energy of a particle in a semi-spherical bowl can be affected by the mass of the particle, its velocity, the shape and depth of the bowl, and the force of gravity.

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