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I need help creating a thesis and an outline on The Calculation of the Coefficient of Friction Using Projectile Motion. Prepare this assignment according to the guidelines found in the APA Style Guide. An abstract is required. The surface beneath the tube was lined with white paper on top of which a carbon paper was laid.The distance between the tube and the table and the ground were measured using a standard measuring tape.Several identical steel balls of measured mass (weighing machine) were taken.A laser pointer was taken and adjusted so that the laser’s beam would pass through the axis of the tube.
Analysis of the experimental setup
The ball falls through the tube due to gravitational acceleration. however, it also experiences friction while moving through the line. We note that:
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While falling through the tube, the potential energy of the balls gets converted to kinetic energy. Also accounting for the loss due to friction, the conservation of energy gives that:
Where W is the energy expended due to friction.
. .(Kleppner & kolenklow, 2010)
Where µ is the coefficient of friction between the ball and the surface of the tube.
Thus, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solving for v,
Solving for v,
This gives the velocity of the ball while exiting the tube. After this, the ball is a projectile. The maximum distance traveled in the y-direction must be equal to the height of the tube H. Thus,
Or the time of projectile transit t is given by:
And therefore, the displacement of the ball in the x-direction is given by:
Also, solving for v in terms of x, it can be shown that:
This value of velocity has been obtained by the direct application of Newton’s laws of motion. This must be the same as the value obtained by the natural energy calculation. Thus,
Using the relation,
But this must be proportional to the work done by the normal force acting between the ball and the surface, that is.
Independent, dependent, and control variables
The independent variable is the variable that we change during the experiment. The dependent variables change their values when we change the independent variable. Control variables are kept constant throughout the investigation to nullify any effects that they may have on the result.
We note that the only variable that we change during the experiment is the tilt of the tube. In this experiment, this is adjusted by changing L’s value, which is related to the Tangent of the angle by the relation Ltanq=H. This, in turn, changes both the distance of projectile fall x and the value of frictional force by the association established above. Thus, the amount of the energy lost due to friction W is a dependent variable, and so is the distance of projectile fall (x). Both of these variables are related to the independent variable L by the relationship established above. The mass of the ball (m) and the height of the table (H) remain unaltered during the experiment and are the control variables.