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Two different balls are rolled (without slipping) toward a common finish line. Ball 1 has an angular speed of ????1=23.2 rad/s, and ball 2 has an angular speed of ????2=14.8 rad/s. The first ball, which has a radius of 0.0663 m, is rolling along a conveyor belt that is moving at 1.19 m/s and starts out 8.57 m from the finish line. The second ball has a radius of 0.0488 m and is rolling along the stationary floor. Two balls are vertically offset and are rolling with clockwise angular speed towards a vertical finish line to the right. Ball 1 rolls with an angular speed of omega subscript 1 on a conveyor belt above ball 2. Arrows indicate that the top surface of the conveyor belt that ball 1 is on moves to the right, while the bottom surface of the conveyor belt moves to the left. Ball 2 rolls with an angular speed of omega subscript 2 on a stationary floor. If the second ball starts out 5.84 m from the finish line, how long does each ball take to reach the finish li

Respuesta :

aabdulsamir

Answer:

Ball 1 = 3.14s , ball 2 = 8.11s

Explanation:

ω₁ = 23.2rad/s

ω₂ = 14.2 rad/s

r₁ = 0.0663m

r₂ = 0.0488m

S = 8.57m

u = 1.19m/s

Assuming conveyor belt is moving towards the finish line,

W = v + u

v = ωr

ωr + u

(ω₁ * r₁ ) + v = (23.9 * 0.0663) + 1.19 = 2.728m/s

Angular velocity (ω) = distance moved (s) / time taken to complete 1 revolution

ω = s / t

t = s / ω

t = 8.57 / 2.728

t = 3.14s

For ball 2, the ball starts 5.54m from the finish line,

W = v + o (since there's no longer initial velocity)

ωr = v

V = 14.2 * 0.0488

V = 0.683 m/s

Velocity = distance / time

V = s / t

t = s / v

t = 5.54 / 0.683

t = 8.11s

annyksl

The first ball will take 3.14 seconds to reach the finish line, while the second ball will take 8.11 seconds.

We can arrive at this answer as follows:

  • First, we'll calculate the width of the belt where the balls will run. This will be done with the following formula:

[tex]W=v+u\\\\v=\omega*r[/tex]

  • So, for the first ball, we use this formula as follows:

[tex]W= (\omega*r)+u\\W=(23.9 * 0.0663) + 1.19\\W= 2.728m/s[/tex]

  • From this result, we can estimate the time the first ball will reach the finish line with the following formula:

[tex]t=\frac{s}{\omega} \\t= \frac{8.57}{2.728} \\t= 3.14s[/tex]

Now we can repeat the same formulas for the second ball, but we must take into account that this ball started running at 5.54m away from the finish line, besides, we don't have the initial speed value.

  • With that, we will use the formulas as follows:

[tex]W= v\\W= \omega*r\\W= 14.2 * 0.0488\\W=V= 0.683 m/s\\\\\\t= \frac{s}{v}\\t= \frac{5.54}{0.683} \\t= 8.11s[/tex]

With this, we could conclude that the first ball would reach the finish line after 3.14 seconds, while the second ball would arrive after 8.11 seconds.

More information:

https://brainly.com/question/17554081?referrer=searchResults

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