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Chapter 8: Q. 64 (page 202)

In Problems 64 and 65 you are given the equation used to solve a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation. Besure that the answer your problem requests is consistent with the equation given.
b. Finish the solution of the problem.
60 N = (0.30 kg)ω2(0.50 m)

Short Answer

Expert verified

a) A ball of mass 300 gm , attached to a string , is rotating around a horizontal circle of 0.5 m radius. The tension on the string is 60 N . Find the angular velocity of the ball.

b) Angular velocity is 20 rad/sec or 190.985 rmp.

Step by step solution

01

Part(a) Step 1 : Given information

The equation given is 60 N = (0.30 kg)ω2 (0.50 m)

02

Part(a) Step 2 : Explanation

Lets observe the equation given 60 N = (0.30 kg)ω2 (0.50 m)

We have Force =60 N. Mass 0.3 kg and radius 0.5 m. Angular velocity is unknown.

We can state problem as

A ball of mass 300 gm , attached to a string , is rotating around a horizontal circle of 0.5 m radius. The tension on the string is 60 N . Find the angular velocity of the ball.

03

Part(b) Step 1 : Given information

The equation given is 60 N = (0.30 kg)ω2 (0.50 m)

04

Part(b) Step 2 : Explanation

The centripetal force acting on a mass m revolving with angular speed ωaround a circle of radius r is given by mω2 r.

The angular velocity of the ball is calculated as

60N=(0.30kg)ω2(0.50m)ω2=60N(0.30kg)(0.50m)ω=20rad/s

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Most popular questions from this chapter

A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving
upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before it broke?

a. An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle u. Find an expression for the angular velocityv.

b. A student ties a 500g rock to a1.0-m-long string and swings it around her head in a horizontal circle. At what angular speed, in rpm, does the string tilt down at a10° angle?

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 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 5.0 N. A
very sharp knife is suddenly inserted, as shown in FIGURE P8.56,to cut the string directly below the point of support. How far to the right of where the string was cut does the ball hit the floor?

The 10 mg bead in FIGURE P8.48 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity ω. If ω is less than some critical value ωc the bead sits at the bottom of the spinning loop. When ω > ωc the bead moves out to some angle θ

  1. What is ωc in rpm for the loop shown in the figure?
  2. At what value of ωc in rpm is θ=30o
See all solutions

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