Physics Lab: The Hooke’s Law and SHM
Hooke’s Law is the law at which explains how the force exerted by an elastic device varies as the elastic device compresses and stretches. In order to mathematically analyze the force the equilibrium position is when the spring is at rest. When force is applied and the spring is being stretched the spring has the tendency of pulling back to the equilibrium position and vice versa. If the force applied to the spring causes it to compress the spring will push back and try to bring it back to equilibrium position. In both examples the direction of the force exerted by the spring is opposite to the direction of the force applied to the spring. The Hooke’s Law is the magnitude of the force exerted by a spring is directly proportional to the distance the spring has moved from equilibrium. The springs that obeys the Hooke’s Law is called an ideal spring because it contains no friction externally or internally. The force constant is (k) the proportionality constant if a spring. The equation Fx=-kx. Fx representing the force exerted by the spring, x is the position of the spring relative to the equilibrium and k as the force constant of the spring. For example springs that require a larger force to stretch or compress them have a large k values. According to the law if x is greater than 0 then Fx is less than 0. If the spring is stretched in the positive direction it pulls in the opposite direction. If the spring is compressed in the negative direction it pushes in the opposite direction. “-kx” is the force exerted by the spring, according to N3LM “+kx” if the force that was applied to stretch or compress it to position x. Hooke’s law for the force applied to a spring is Fx=kx. Even though this law has been referring to springs only, this law can apply to any elastic device. Elastic Potential Energy is energy that is stored in objects that are stretched, compressed, bent or twisted. To find an equation for elastic potential energy we consider the work done on an ideal elastic device that is being stretched or compressed. The area under the line on a force-displacement graph indicates the work. Since the force applied to an ideal spring depends on the displacement the area of the graph is a triangle. The final equation is W=1/2x (kx) then shortened into W=1/2kx2. The W representing work, k is the force constant of the elastic device and x is the amount of stretch or compression from the equilibrium position. Since work has been transformed into elastic potential energy we can write the equation as Ee=1/2kx2. The elastic potential energy can then be transformed into a lot of different energy types such as kinetic energy, sound energy or gravitational potential energy. Simple Harmonic Motion is the periodic vibratory motion in which the force and acceleration is directly proportional to the displacement. SHM is a combination of Hooke’s Law and N2LM. Parameters of SHM may include the amplitude (A), period (T), frequency (f), position, velocity (v) and acceleration (a). Period and Frequency can be calculated with T= 2πmk or f= 1/2πmk. According to the LCE when mass is released the total energy of the system is the sum of elastic potential energy in the spring and the kinetic energy. The equation ET=1/2 kx2+1/2mv2. Damped harmonic motion is periodic or repeated motion in which the amplitude of vibration and the energy decreases with time. Purpose
In this lab we are testing real springs to determine under what conditions, if any, they obey Hooke’s Law. We are also exploring what happens when force constant of the springs are linked together either by the weight or the springs itself. This lab is to explore the difference between different springs and how it affects the force constant, displacement, frequency, total energy, amplitude and elastic potential energy. We also examine how the different masses affect the force constant, displacement,...
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