A small object of mass m is located on the surface of the disk with radius R if the magnitude of the coefficient of static friction between the object and the disc is u and the disc rotates with a certain angular speed so that the object of mass m slides from the disc which is at a height h. Prove that the horizontal distance traveled by the object is x = VµR2h

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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1. A small object of mass m is located on the surface of the disk with radius R if the
magnitude of the coefficient of static friction between the object and the disc is u and
the disc rotates with a certain angular speed so that the object of mass m slides
from the disc which is at a height h. Prove that the horizontal distance traveled
by the object is
x = JuR2h
2. A child of mass 80 kg sits on a spinning disc and begins to slide if the
coefficient of friction is 0.5 and the angular velocity of the rotating disc is
10rad/s. calculate the maximum radius R provided that the child can still sit
and remain on the spinning disc? Compare your answer with the manual
solution and use Matlab
A beautiful jumper with mass m jumps from a height of 10 m (a
Calculate the initial velocity V at the time of the diver's collision with the water and the
estimated time from the time of the dive to the collision. Assume that the buoyant force of the
water is able to balance the magnitude of the gravitational force on the diver and the
viscous force on the diver. formulated by
(b) Determine the equation of motion when the diver is in free fall. Construct the
velocity function Vas a function of the depth x under the water provided that V = Vo at x =
Om
(c) if the magnitude is b/m = 0.4 m-1, find the depth reached if V = Vo/10 (d)
Determine the equation for the time-dependent depth.
4. The frictional force between air and a person riding a bicycle is defined by
F-av where V is velocity and a 4 newton-sec/m. At maximum, the
driving power is 600 watts. Analyze the value of the maximum speed in the
horizontal direction without wind? Compare your answer with the manual solution
and use Matlab
Transcribed Image Text:1. A small object of mass m is located on the surface of the disk with radius R if the magnitude of the coefficient of static friction between the object and the disc is u and the disc rotates with a certain angular speed so that the object of mass m slides from the disc which is at a height h. Prove that the horizontal distance traveled by the object is x = JuR2h 2. A child of mass 80 kg sits on a spinning disc and begins to slide if the coefficient of friction is 0.5 and the angular velocity of the rotating disc is 10rad/s. calculate the maximum radius R provided that the child can still sit and remain on the spinning disc? Compare your answer with the manual solution and use Matlab A beautiful jumper with mass m jumps from a height of 10 m (a Calculate the initial velocity V at the time of the diver's collision with the water and the estimated time from the time of the dive to the collision. Assume that the buoyant force of the water is able to balance the magnitude of the gravitational force on the diver and the viscous force on the diver. formulated by (b) Determine the equation of motion when the diver is in free fall. Construct the velocity function Vas a function of the depth x under the water provided that V = Vo at x = Om (c) if the magnitude is b/m = 0.4 m-1, find the depth reached if V = Vo/10 (d) Determine the equation for the time-dependent depth. 4. The frictional force between air and a person riding a bicycle is defined by F-av where V is velocity and a 4 newton-sec/m. At maximum, the driving power is 600 watts. Analyze the value of the maximum speed in the horizontal direction without wind? Compare your answer with the manual solution and use Matlab
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