A cart on a track is connected to a spring with a k value of k= 15.3 N/m. It is

Question

A cart on a track is connected to a spring with a k value of k= 15.3 N/m. It is pulled back 0.5 m and released, causing it to oscillate at a rate of one cycle every 4.4 seconds. Complete the tables below, drawing the analogy between the cart and a ball on a turntable.

ROTATOR:

Radius  m
Angular Velocity  rad/s
Linear Velocity  m/s
Time for one rotation  s
Centripetal Force  N

OSCILLATOR:

Amplitude  m
Max Velocity  m/s
Period  s
Frequency  Hz
Max Spring Force  N
Spring Constant  N/m

Cart Mass:  kg

Explanation / Answer

T = 4.4 sec

w = 2pi / T = 1.43 rad/s

Rotator:

Radius :

F = k x = (15.3)(0.5) = 7.65 N

F= m w^2 r

r = 3.74 / m

Angular velocity:

w = 1.43 rad/s

Linear velocity:

v= w r = 5.35 / m

Time for one rotation:

T = 4.4 s

Centripetal force :

F = 7.65 N

OSCILLATOR:

amplitude : A = 0.5 m

Max velocity: Vmax = A w = 0.715 m/s

Period : T = 4.4 s

frequency, f = 1/T = 0.227 Hz

Max spring force : Fmax = k A = 7.65 N

Spring constant = 15.3 N/m

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