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Q.32

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 200

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Short Answer

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 .

See the step by step solution

Step by Step Solution

Step 1: Given Infromation (Part a)

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

Step 2: Explanation (Part a) 

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 for

Step 5: Final Answer  (part a)

An expression for .

Step 6: Given Infromation (Part b)

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

Step 7: Explanation (Part b)

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:

Step 9: Calculate the net force on the bead

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

Step 7: Final Answer

The component form of the force is

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