Question

A spring scale on a rotating platform indicates that the horizontal force on a 0.621 kg mass is 1.14 N when the mass is 2.30 m from the axis of rotation. How long does it take for the platform to make one revolution?

Answer 1

By F = mv^2/r
=>F = mr?^2 [as v = r?]
=>? = ?F/mr
=>? = ?[1.14/(0.621 x 2.30)
=>? = .8933 rad/sec
=>2?/T =.8933
=>T = (2 x 3.14)/.8933
=>T = 7.03 sec

Answer 2

F = m w^2 R where w is the angular velocity in radians per sec.
From this you get f/(mR)= w^2
w= sqrt(F/mR)

w = 2Pi/T or T = 2 Pi/w

So first find w
F= 1.14
m= 0.621
R= 2.3

substituting we get w= sqrt( 1.14/(0.621*2.3)
= 0.8934 radians per sec

substitute into T= 2 Pi / w
= 7.029 secs per turn

Answer 3

m=0.621 kg

H = 1.14 N

H=ma

a=1.14/0.621 = 1.836 m per square sec

a = vxv/r

V = sqrt( a xr)

v= sqrt (1.836 x 2.3)

=2.054 m/sec

W=v/r

=2.054/2.3=0.8933

T=2 $\pi$ /w =2x3.14 / 0.8933

=7.03 sec