Answer:
To solve this problem, you can use the following formulas:
Velocity (v) = 2πr * f
Acceleration (a) = v^2 / r
Centripetal force (F) = ma
In these formulas, r is the radius of the circle, f is the frequency of the circular motion, and m is the mass of the object.
a) To find the velocity of the mass, you can substitute the values given into the formula for velocity:
v = 2πr * f
= 2π(0.25 m) * 2.0 Hz
= 1.57 m/s
So, the velocity of the mass is approximately 1.57 m/s.
b) To find the acceleration of the mass, you can substitute the values given into the formula for acceleration:
a = v^2 / r
= (1.57 m/s)^2 / 0.25 m
= 4.45 m/s^2
So, the acceleration of the mass is approximately 4.45 m/s^2.
c) To find the centripetal force acting on the mass, you can substitute the values given into the formula for centripetal force:
F = ma
= 1.5 kg * 4.45 m/s^2
= 6.68 N
So, the centripetal force acting on the mass is approximately 6.68 newtons.