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Chapter 8: Q. 69 (page 203)

A small bead slides around a horizontal circle at height y inside the cone shown in FIGURE CP8.69. Find an expression for the bead’s speed in terms of a, h, y, and g.

Short Answer

Expert verified

The expression for velocity is v=ahgy

Step by step solution

01

Given Information

A small bead slides around a horizontal circle at height y inside the cone .

Radius of base of cone = a

Height of cone = h

02

Explanation

Lets draw Free Body diagram as below

From the diagram equation vertical and horizontal components of force

Rsin(θ)=mg..........................(1)and,Rcos(θ)=mv2r................................(2)

Divide equation(1) by (2) we get

mv2rmg=Rcos(θ)Rsin(θ)v2rg=tan(θ)..........................(3)

From the diagram we can get angle

ry=ahr=ayhtan(θ)=ah…………………………(4)

From equation (3) and (4)

v2=grtan(θ)v2=gayhahv2=a2gyh2v=ahgy

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Most popular questions from this chapter

The weight of passengers on a roller coaster increases by 50% as the car goes through a dip with a 30m radius of curvature. What is the car’s speed at the bottom of the dip?

A concrete highway curve of radius 70mis banked at a 15°angle. What is the maximum speed with which a 1500kg rubber tired car can take this curve without sliding?

A highway curve of radius 500m is designed for traffic moving at a speed of 90km/h. What is the correct banking angle of the road?

A golfer starts with the club over her head and swings it to reach maximum speed as it contacts the ball. Halfway through her swing, when the golf club is parallel to the ground, does the acceleration vector of the club head point (a) straight down, (b) parallel to the ground, approximately toward the golfer’s shoulders, (c) approximately toward the golfer’s feet, or (d) toward a point above the golfer’s head? Explain.

A 500 g steel block rotates on a steel table while attached to a 1.2-m-long hollow tube as shown in FIGURE CP8.70. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 4.0 N perpendicular to the tube.

The maximum tension the tube can withstand without breaking is 50 N. If the block starts from rest, how many revolutions does it make before the tube breaks?
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