Forces - 4 - Hooke's Law | High School

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High School Physics
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2024
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Forces 2.6 Hooke’s Law Hooke: ⚫ In 1678, Robert Hooke published the results of his work on elasticity and the deformation of an elastic object. ⚫ An object is said to be elastic if it returns to its original dimensions after the applied force is removed. low k = easy to stretch Hooke’s Law: ⚫ The amount of deformation of an elastic object is directly proportional to the force applied to deform it. F = kx F = force applied on spring (N) k = force constant of the spring (N/m) x = amount of deformation of the spring (m) Ex. A spring has a force constant of 0.020N/m. What force is exerted to stretch the spring 12cm? F = kx F=? F = (0.020)(0.12) k = 0.020 N/m F = 2.4x10-3N x = 0.12m Ex.1 A 31.0 N force stretches a bungee cord 43.0 cm. What is the force constant of the cord? F = kx F = 31.0N 31 = (?)(0.430) k=? k = 72.1 N/m x = 0.430m Ex.2 A spring that has an original length of 0.125m is stretched to a total length of 0.173m when a force of 3.60N is applied to it. What is the force constant of this spring. F = kx 3.60 = (?)(0.048) F = 3.60N k = 75 N/m k=? x = 0.048m 0.173 – 0.125 = 0.048m Ex. A 325 g mass is applied to a spring with a force constant of 5.0 N/m. How much does it stretch? F = mg F = kx F=? m = 0.325kg F = 3.185 N k = 5.0 N/m g = 9.80 N/kg x=? F = (0.325)(9.8) 3.185 = (5)(x) F = 3.185 N x = 0.64 m Ex.3 in N A mass of 500.0g stretches a spring 8.0cm when it is attached to it. What additional weight would you have to add so that the spring would stretch 10.0cm? F = mg F = kx F = kx F = (0.500)(9.80) 4.90000 = (k)(0.080) F = (61.25)(0.1) F = 4.900 N k = 61.250 N/m F = 6.125 N 6.125 N – 4.900 N = Fadditional F = 1.225 N → 1.2 N F = mg → 1.225 N ÷ 9.8 = 0.1250 kg = ~130g Ex.4 The following graph describes the spring constant of three different springs. A B Force (N) C length (m) Which of the springs would be the easiest to stretch? F = kx F k= x •small slope = low k k = slope •low k = easy to stretch spring C is easiest to stretch HW: pg 368 # 7, 8, 11 & 16 Quantum