   Chapter 5, Problem 71AP

Chapter
Section
Textbook Problem

A 2.00 × 102-g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 30.0 cm (Fig. P5.71). Calculate (a) its gravitational potential energy at A relative to B, (b) its kinetic energy at B, (c) its speed at B, (d) its potential energy at C relative to B, and (e) its kinetic energy at C. Figure P5.71 Problems 71 and 72.

(a)

To determine
The gravitational potential energy at A relative to B.

Explanation

Given Info:

Mass of the particle is 2.00×102g .

Radius of the hemisphere bowl is 30.0cm .

Consider the h=0 point at the lowest point of the bowl. Then,

hA=R

hB=0

hC=23R

• R is the radius of hemisphere bowl

Since, the bowl is smooth; there is no friction force acting on the particle. Hence, the mechanical energy is conserved.

(KE+PEg)f=(KE+PEg)i

Formula to calculate the gravitational potential energy at A is,

(PEg)A=mghA

• m is the mass of the particle
• g is acceleration due to gravity
• hA is the height of point A

Substitute 2

(b)

To determine
The kinetic energy of the particle at B.

(c)

To determine
The speed of the particle at B.

(d)

To determine
The potential energy of the particle at C relative to B.

(e)

To determine
The kinetic energy of the particle at C.

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