Unit 7 Hooke\'s Law and Simple Harmonic Motion (This is the Signature assignment

Question

Unit 7 Hooke's Law and Simple Harmonic Motion (This is the Signature assignment. Bring thumb drive for this lab.) Pre-lab: This prelab is worth 15 points. 1) State Hooke's law. Write the equation for it and define each variable. (2) Write down the equation for the time period of an object of mass M hooked horizontally b) vertically, by a spring of spring constant "k" in a gravitational field strength ‘g'. 2) a) Using the equation for Hooke's law, outline the steps you would utilize to determine the value of 'k' for the object hanging vertically. (3) 3) When you plot the displacement along x-axis and the applied force along y-axis for a mass hanging vertically by a spring, the area under the curve represents a physical quantity. What would this quantity be and what does it mean in a physical sense? (1) 4)

Explanation / Answer

1. hookes law states that the extension in a material upto a limit is directly proportional to the force aspplied to the material. The constant of proportionality is called elasticity modulus of the material and the limit upto which hooke's law holds is called the elastic limit of the material

2. for an object of mass M hooked to a spring of spring constant k

the time period is given by T = 2*pi*sqroot(m/k) irrespective of horizontal or vertical alignment of the setup

3. for an object hanging vertically for given mass, m the deflection measured of the spring from the normal length be a

then from hookes law

mg = ka

or k = mg/a

4. for a graph plotted between force applied and the displacement of the spring

the force applied F = kx

area under graph

0.5*kx*x = 0.5kx^2

this area represents the energy stored in the spring due to extension

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