The speed of the block is given by:
[tex] V = w * R
[/tex]
Where,
w: angular speed
r: radius of the circular path.
The angular velocity must be in radians over seconds:
[tex] w = (75) * (2\pi) * (\frac{1}{60})
w = 7.85
[/tex]
The radius must be in the subway:
[tex] R = (50) * (\frac{1}{100})
R = 0.5 m
[/tex]
Then, the speed is given by:
[tex] V = (7.85) * (0.5)
[/tex]
[tex] V = 3.925 \frac{m}{s}
[/tex]
The tension of the rope is the centripetal force.
By definition, the centripetal force is:
[tex] F = m * (\frac{V^2}{R})
[/tex]
Where,
m: mass of the block in kilograms
Substituting values:
[tex] F = 0.2 * (\frac{3.925 ^ 2}{0.5})
F = 6.2 N
[/tex]
Answer:
its speed and tension on string are:
[tex] V = 3.925 \frac{m}{s}
F = 6.2 N [/tex]
