Particle A and B are traveling around a circular track in clockwise direction at a speedof 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, determinehow long it takes for a collision to occur. How many full circles of turn has eachparticle completed before colliding? What is the magnitude of the acceleration ofeach particle just before the collision occurs?0 = 120°r= 5 mらや

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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Question

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,

$ϕ = ϕ_{0} + ω t (1)$

Where $ϕ_{0}$ 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,

$ω = \frac{v^{2}}{r} (2)$

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

$\frac{d v (t)}{d t} = a \int_{v (0)}^{v (t)} d v = \int_{t = 0}^{t} a d t v (t) - v (0) = \int_{t = 0}^{t} a d t v (t) = v (0) + \int_{t = 0}^{t} a d t (3)$

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