Circular Motion - Physics

Question

A) A toy is on a horizontal rotating surface. It is positioned 0.25m from the center of the circle and it makes one complete revolution every 0.75s. If the force of friction is 8.0N, How much is the car's mass?

 

b) A pendulum has a string with a length of 0.75m  Determine the acceleration due to gravity on a planet on which this simple pendulum has a frequency of 0.4 Hz

Answer 1

Given

Length of the string L = 0.75 m

Frequency f = 0.4 Hz

Calculate the time .

T=2π /f

  = 2π / 0.4

   = 15.71 s

Calculate the acceleration due to gravity on a planet by using the simple pendulum formula:

 g = 4 π²L/T ²

    = 4 π²(0.75) / (15.71) ²

    = 0.12 m/s²

 

 Therefore, the acceleration due to gravity on a planet is 0.12 m/s²

 

Answer 2

a)

Calculate the angular velocity,

ω = θ/t

    = 2π /0.75

    =8.381 rad/s

Calculate the acceleration of toy in circular path,

a = r ω²

   =( 0.25) (8.381)²

   =17.56 m/s²

Calculate the mass of the toy by using the newton's second law,

F = ma

m = F/ a

   = 8 / 17.56

   = 0.456 kg

   =456 g

Therefore, the mass of the toy is 456 g