Question

You have developed a method in which a paint shaker is used to measure the coefficient of static friction between various objects and a known surface. The shaker oscillates with a fixed amplitude of 45 mm , but you can adjust the frequency of the motion. You have affixed a horizontal tabletop (the known surface) to the shaker so that the tabletop oscillates with it. Then you put an object on the tabletop and increase the frequency until the object begins to slip on the surface.If a frequency f = 1.85 Hz is required before a penny positioned on the tabletop starts to slide, what is the coefficient of static friction between penny and tabletop?

Answer 1

Answer:

0.62

Explanation:

A = Amplitude

f = Frequency = 1.85 Hz

$\mu$ = Coefficient of static

g = Acceleration due to gravity = 9.81 m/s²

Angular frequency

$\omega=2\pi f\\\Rightarrow \omega=2\pi\times 1.85$

Maximum acceleration

$a_{max}=A\omega^2\\\Rightarrow a_{max}=0.045\times (2\pi\times 1.85)^2$

$a_{max}=\mu g\\\Rightarrow \mu=\frac{a_{max}}{g}\\\Rightarrow \mu=\frac{0.045\times (2\pi\times 1.85)^2}{9.81}\\\Rightarrow \mu=0.62$

Coefficient of static friction between penny and tabletop is 0.62