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Particle A and B are traveling around a circular track in clockwise direction at a speed of 8 m/s at the instant shown. If the speed of B is increasing by (a,)B = 1 m/s² , and at the same instant A has an increase in speed of (a¿)a = 0.8 t m/s², determine %3D %3D how long it takes for a collision to occur. How many full circles of turn has each particle completed before colliding? What is the magnitude of the acceleration of each particle just before the collision occurs? 0 = 120° 1= 5m

Particle A and B are traveling around a circular track in clockwise direction at a speed of 8 m/s at the instant shown. If the speed of B is increasing by (a,)B = 1 m/s² , and at the same instant A has an increase in speed of (a¿)a = 0.8 t m/s², determine %3D %3D how long it takes for a collision to occur. How many full circles of turn has each particle completed before colliding? What is the magnitude of the acceleration of each particle just before the collision occurs? 0 = 120° 1= 5m

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Particle A and B are traveling around a circular track in clockwise direction at a speed of 8 m/s at the instant shown. If the speed of B is increasing by (a)B = 1 m/s² , and at the same instant A has an increase in speed of (a¿)A = 0.8 t m/s², determine how long it takes for a collision to occur. How many full circles of turn has each particle completed before colliding? What is the magnitude of the acceleration of each particle just before the collision occurs? 0 = 120° r= 5 m らや
Transcribed Image Text:Particle A and B are traveling around a circular track in clockwise direction at a speed of 8 m/s at the instant shown. If the speed of B is increasing by (a)B = 1 m/s² , and at the same instant A has an increase in speed of (a¿)A = 0.8 t m/s², determine how long it takes for a collision to occur. How many full circles of turn has each particle completed before colliding? What is the magnitude of the acceleration of each particle just before the collision occurs? 0 = 120° r= 5 m らや
Expert Solution
Step 1

Let the initial position of particle B be the x axis, the two particles then collide at the instant when clockwise angles they make with x-axis are equal.

 

The angular position is given by,

ϕ=ϕ0+ωt        (1)

Where ϕ0 is the initial angle and ω is the angular velocity.

The angular velocity of a particle moving on a circle of radius r is given by,

ω=v2r         (2)

 

Given the acceleration and initial velocity the final velocity can be found by integrating the acceleration equation as,

dv(t)dt=a∫v(0) v(t) dv=∫t=0tadtv(t)-v(0)=∫t=0tadtv(t)=v(0) +∫t=0tadt                     (3)

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