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