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ex11 - EXPERIMENT 11 The Spring Hooke's Law and...

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1 EXPERIMENT 11 The Spring Hooke’s Law and Oscillations Objectives To investigate how a spring behaves when it is stretched under the influence of an external force. To verify that this behavior is accurately described by Hooke’s Law. Measure the spring constant, k in two independent ways Apparatus A spring, photogate system, and masses will be used. Theory Hooke's Law An ideal spring is remarkable in the sense that it is a system where the generated force is linearly dependent on how far it is stretched. Hooke's law describes this behavior, and we would like to verify this in lab today. In order to extend a spring by an amount Δ x from its previous position, one needs a force F which is determined by F = k Δ x. Hooke’s Law states that: F S = -k Δ x (1) Here k is the spring constant which is a quality particular to each spring and Δ x is the distance the spring is stretched or compressed. The force F S is a restorative force and its direction is opposite to the direction of the spring’s displacement Δ x. To verify Hooke’s Law, we must show that the spring force F S and the distance the spring is stretched Δ x are proportional to each other (that just means linearly dependant on each other), and that the constant of proportionality is -k. In our case the external force is provided by attaching a mass m to the end of the spring. The mass will of course be acted upon by gravity, so the force exerted downward on the spring will be F g = mg. See Figure 1. Consider the forces exerted on the attached mass. The force of gravity (mg) is pointing downward. The force exerted by the spring (-k Δ x) is pulling upwards. When the mass is attached to the spring, the spring will stretch until it reaches the point where the two forces are equal but pointing in opposite directions : F s – F g = 0

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2 or mg = -k Δ x (2) This point where the forces balance each other out is known as the equilibrium point . The spring + mass system can stay at the equilibrium point indefinitely as long as no additional external forces come to be exerted on it. The relationship in (2) allows us to determine the spring constant k when m, g, and Δ x are known or can be measured. This is one way in
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ex11 - EXPERIMENT 11 The Spring Hooke's Law and...

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