A merry-go-round is stationary. A dog is running around the merry-go-round on th

Question

A merry-go-round is stationary. A dog is running around the merry-go-round on the ground just outside its circumference, moving with a constant angular speed of0.780rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the edge of the merry-go-round one-third of a revolution in front of him. At the instant the dog sees the bone (t= 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of0.016 2rad/s2.

(a) At what time will the dog first reach the bone?

(b) The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time?

Explanation / Answer

One third of a revolution =120 degrees

angular velocity of dog w=0.780 rad/s

Angular acceleration of merry-go-round a=0.0162

So using equation of kinematics Theta=w*t+0.5*a*t^2

here theta=120 degrees=2*pi/3 radians

w,a are given.putting them in above equation gives two values of t.Th epositive value must be chosen as time cannot be negative

The value of t=2.612 seconds

For the second part,the dog completes a one and one third of a revolution So thets now=2*pi+2*pi/3

So time required is 9.748 seconds.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.