Question

A mass of 1.5 kg moves in a circle of radius 25 cm at 2.0 Hz. Calculate:

a) the velocity. b) the acceleration. c) the centripetal force acting on the mass.

Answer 1

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.