BridgeMechanicsFree

The Bouncing Coin

SHM and oscillations

A kitchen scale has a light pan supported on a vertical spring. With a load on the pan, the total oscillating mass is

m = 0.250\ \text{kg}

and the spring is compressed by its static deflection

e = 4.90\ \text{cm}

from its natural length when the pan is at rest at equilibrium. A small coin, whose mass is negligible compared with

m

, rests loosely on top of the load. The pan is pushed down a further

A = 3.00\ \text{cm}

below equilibrium and released, so that it performs vertical simple harmonic motion of amplitude

A

. Ignore air resistance and damping.

Data: g = 9.81 m s⁻² · g on the Moon = 1.62 m s⁻²

(a)

show that2 marks

Show that the period of oscillation is

T = 2\pi\sqrt{\dfrac{e}{g}}

, and calculate its value.

(b)

calculate2 marks

Calculate the maximum speed and the maximum acceleration of the pan. State where in the motion each maximum occurs, and explain, in terms of the net force on the pan, why they do not occur at the same point.

(c)

explain2 marks

By considering the forces acting on the coin, explain where in the cycle the coin is most likely to lose contact, and show that it just stays in contact for all amplitudes up to

A_{\max} = e

(d)

explain2 marks

The same scale and load are taken to the Moon. State which quantities stay the same and which change, calculate the new static deflection, and explain why the period is unchanged even though

T = 2\pi\sqrt{e/g}

contains

g

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