4AHookesLaw.docVIP

Experiment 14: Hooke’s Law and Simple Harmonic Motion Purpose (1) To study Hooke’s Law for an elastic spring (2) To study Simple Harmonic Motion of a mass suspended from an elastic spring Apparatus Helical steel spring with supporting stand and scale, set of slotted weights with hanger, timer, laboratory balance. Theory: Hooke’s Law A spring exerts a force which is given by Hooke’s Law: 1 Fs = - kx where x is the amount of displacement from the equilibrium position. The negative sign in this equation shows that the spring’s force is opposite to x. If the spring is stretched (x is positive) then the spring pulls back. If the spring is compressed (x is negative) the spring pushes. The parameter k is the spring constant and is a property of the spring. It is different for different springs. An elastic spring subjected to a stretching force of magnitude F will be stretched from its equilibrium position by an amount x given by Hooke’s Law until the spring force, which pulls back when the spring is stretched, balances the stretching force. If you hang your spring on the supporting stand (Figure 1), it will be at its unstretched length. Hanging a slotted weight of mass mload on it will subject it to the force of gravity on the slotted weight F= mload g. This will cause the spring to stretch a distance x from its equilibrium position according to Hooke’s Law until Fs = mload g. Simple Harmonic Motion (SHM) If a spring with a weight hanging on it is given an additional displacement of magnitude a (Fig. 2) and released, it will undergo Simple Harmonic Motion. In simple harmonic motion a spring will oscillate up and down with an amplitude a and a period T. The minus sign in Hooke’s Law tells us why this happens. When the spring is stretched downward, it pulls upwards and then becomes compressed. When it is compressed, it pushes downward and then becomes stretched, and so on. The equation for period T is: 2 T = 2( Meff