Energy Equations Lab

Rebecca, Joe, Alondra

Elastic Interaction Energy

VM: As the displacement increases, the force of the spring increases proportionally.

MM: Fs = 0.1(N/cm)(deltaX) - 0.02N

Slope: For every 1 cm of displacement, there is 0.1 Newtons of force.

Y-int: When there is no displacement, there should be no force. The intercept is close enough to 0 to be negligible.

General Equation:

Fs = k(displacement)

       k = the "spring constant" or the "stretchiness" of the spring
This equation is called Hooke's Law, saying that the stretch of the spring is proportional to the force of the spring. Springs that follow this law are called "Hookean springs"
The slope physically represents how stretchy the spring is. For instance, the spring inside a pen is not very tightly wound, so t has a relatively low spring constant. The springs inside a car have to have a very high spring constant in order to perform at maximum capacity and safety.

Area represents the elastic energy. The equation, when integrated, gives us the energy of the spring in joules. In order to find this equation, we calculated the area by calculating the area of a triangle.
Area = 1/2 bh
Ee = 1/2(deltaX)(Fs)
Fs = k(deltaX), therefore:
Ee = 1/2 k(deltaX)^2
The units are joules because Energy = N/m x m^2, meaning that Energy = N x m, which we call joules.

Gravitational/Kinetic Interaction

The area under the graph of the gravitational interaction represents the gravitational energy. Its equation, as derived form the area equation of length x width, or Eg = Fa(deltaX), Fa is equal to the force of gravity, which is equivalent to the mass of the object times the gravitational field. Therefore: Eg = mgh   (with h being the height, equivalent to the displacement.)

The area under the graph of the kinetic interaction represents the kinetic energy. Its equation, as derived from the area equation of length x width, or Ek = Fa(deltaX), Fa is equal to the mass times the acceleration because the object is accelerating in a positive direction. The displacement is also equal to half the acceleration times the time squared. In the case of acceleration, we can plug in velocity over time for all of the "a" variables, and the time cancels out, leaving the final equation:
Ek = 1/2 mv^2

KOH Eval

I modified my car from the original plans by using sliders instead of wooden wheels, which were screwed in rather than attached via hot glue. The body was plastic, not wood, and the frame wasn't a block, but rather a set of shingles to support the rat trap. Unfortunately, my car did not go up the ramp. It moved, but only slightly because as I was winding it one of the wheels came loose. This made it impossible for the car to move because the force of the rat trap went into the axle rather than the wheel, and there was no friction between the wheel and the ground to propel the car forward. I think in terms of what went wrong, the wooden axle was too thin and split under the pressure of the screw. I will definitely make further modifications, maybe even construct a whole new car in order to make sure this one doesn't fall apart when I need it most.

Famous Physics Experiments

Experiment 1:
Galileo demonstrated that objects, no matter their mass, fall at the same rate by dropping two balls of different masses from the Leaning Tower of Pisa. They fell at the same time and therefore proved his hypothesis correct and disproved Aristotle's theory of gravity, which was the commonly held belief that an object's rate of freefall was dependent on its mass.
Galileo's experiment was validated by the moon landing, where astronauts demonstrated a feather and a hammer falling at the same rate because of no air resistance.

Experiment 2: Hooke's Law
Robert Hooke discovered the law of elasticity by attaching weights to a spring and measuring how the force and the "stretch" were related. He discovered that they were directly proportional, and that the amount of force applied to the spring was linearly related to the extension of the spring. Not all springs exhibit this, but those that do are called "Hookean" springs.