Q.27

Expert-verified
Found in: Page 257

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# a. In , what minimum speed does a particle need at point A to reach point B?b. What minimum speed does a particle need at point B to reach point A?

(a) Minimum speed at point A =

(b) Minimum speed at point B = .

See the step by step solution

## Step 1 : Speed :

It is the change in an object's location with regard to time.

## Step 2 : (a) Explanation :

Particle's mass ,

Formula to determine the kinetic energy of a particle, ,

= kinetic energy,

= particle's mass,

= particle's velocity.

Consider the graph of potential energy against distance,

The minimal speed necessary by the particle to get from point A to point B is the speed at the top of the graph. The particle's potential energy is at the top of the graph. Calculate the energy difference between the top of the curve and point A.

The change in potential energy is equal to the change in kinetic energy, according to the law of energy conservation. Hence,

Formula to calculate the minimum speed required at point A,

Substitute values in equation,

Hence, the particle's minimum velocity to go from point A to point B is .

## Step 3 : (b) Explanation :

The minimal speed necessary by the particle to get from point A to point B is the speed at the top of the graph. The particle's potential energy is at the top of the graph. Calculate the energy difference between the top of the curve and point B.

The change in potential energy is equal to the change in kinetic energy, according to the law of energy conservation. Hence,

Formula to calculate the minimum speed required at point B,

Substitute the values,

Hence, the particle's minimum velocity to go from point A to point B is .