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Physics 2LC Weight Hanger Meter Stick Photogate Plastic Plate Spring Hooke’s Law and Harmonic Oscillation(Pre lab assignment included) Objective: To experimentally study: Hooke’s Law of elasticity Simple Harmonic motion The static and dynamic description of elastic materials is rooted in two basic concepts: Hooke's Law and Simple Harmonic Oscillation. The elastic behavior of many materials can be described in terms of Hooke's Law, F= -kx.In words: “When an elastic material is stretched or compressed (displaced) from equilibrium by an amount x, the restoring force is proportional to the amount stretched or compressed (displacement).” When we have Hooke's Law, Simple Harmonic Oscillationcan take place. A large spring will be used to verify Hooke's Law, and to measure oscillation periods in a simple harmonic oscillator. The Apparatus: 1.A 2-meter stick attached to a vertical support rod, mounted on the lab bench. 2.A movable clamp with horizontal rod to support the spring and masses. 3.The spring. 4.A clear plastic plate with a black line, used to interrupt the PhotoGate for period measurements. 5.Weight Set consisting of: a)A 50 gram hanger b)Masses of 50 g, 100 g, and 200 g Masses between 50 and 400 grams can be selected, in 50 gram increments. 6. Photogate timer clamped to vertical support rod. 7. Pasco PasPortinterface, Computer with Data Studiosoftware for period measurements and data fitting. CAUTION: DO NOT OVER-STRETCH OR TWIST THE SPRING - IT WILL NOT RETURN TO ITS ORIGINAL LENGTH AND SHAPE.
2 The Physics The basics of Hooke's Law and Simple Harmonic Oscillation are well covered in your text. Following is a brief summary. Physics - Hooke's Law We will use a spring hanging vertically, stretched by weights connected to its lower end. If we neglect the mass of the spring, a free body diagram for the hanging mass gives Ftotal= mg –kx = 0 in equilibrium. The displacement, x, is measured from the equilibrium position of the spring without added mass. In the lab, we will vary the mass mand measure the corresponding displacement x for each mass. Since mg= kx (1) a plot of mgversus xwill have a slope of k, the spring constant. Physics - Simple Harmonic Oscillator A simple harmonic oscillator consisting of a massless spring with constant k, and a mass mwill have a period of oscillation(time taken for one complete cycle)T given by: T2mk(2) If the spring is stiff (large k), the period is less and vice versa. Similarly, a larger masses lead to a larger inertia and a longer T.