Q.32

Expert-verifiedFound in: Page 200

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A bead slides along a frictionless wire with the parabolic shape .

a. Find an expression for , the vertical component of acceleration, in terms of , , and . Hint: Use the basic definitions of velocity and acceleration.

b. Suppose the bead is released at some negative value of and has a speed of as it passes through the lowest point of the parabola. What is the net force on the bead at this instant? Write your answer in component form

a). An expression for .

b). The component form this force is .

A bead slides along a frictionless wire with the parabolic shape .

According to the information, the equation for parabolic shape is :

Differentiating on both sides:

Consider

Where, is the velocity in direction

is the velocity in direction

Therefore,

Again differentiating on both sides:

Consider

Where,

is the acceleration in direction

is the acceleration in direction

Hence, the expression forAn expression for .

A bead slides along a frictionless wire with the parabolic shape .

According to the information,

is the mass of the bead slides

is the velocity in x direction

is the velocity in direction

Here,

Substituting above values:

Let's find the net force on the bead

where, net force

mass

acceleration in the axis

Therefore,

Differentiating on both sides with

Therefore,

The component form of the force is

The component form of the force is

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