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work2 - Work Energy Circular Motion Purpose To apply the...

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Work & Energy, Circular Motion Purpose: To apply the Work-Energy Theorem to a real-life problem. To investigate the forces and accelerations associate with circular motion. Apparatus: Loop De Loop apparatus, stainless steel ball, masking tape, timer, meter stick, Flying Cow hanging from string, spring scale (blue). Introduction This lab consists of two parts, which will involve switching lab desks: - You will predict (theoretical) the minimum height to which a stainless steel ball must be raised such that when it is released it rolls down an incline and into a circular loop and maintains contact with the loop during its circular motion. You will then find out the actual (experimental) height which enables it to do so and try to explain the discrepancy, if any, between theory and experiment. - You will predict the tension in the string attached to a Flying Cow going around in a circle (dynamic). You will then measure the tension in the string indirectly using a spring scale, with the cow stationary (static), compare the results, and reconcile the number of forces identified in each case Theory (optional) The Work-Energy Theorem States that
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(in English) The net work done on an object equals its change in kinetic energy. (in Mathematics) W = KE f − KE i (1) Recall that the kinetic energy of an object is KE = 1 2 mv 2 The work done on an object is given by W = Fcos  s where s is the distance over which the force acts and the angle between the force and the displacement. For a single mass dropping to the floor from height h, the only force doing work (causing motion) is the gravitational force on the small mass, mg, which acts over the distance h, the height from which it drops to the floor. We can now expand on equation (1): mgh = 1 2 mv f 2 1 2 mv i 2 (2) The quantity mgh is the potential energy the mass acquires as it is moved from the floor (zero potential) to its starting point (mgh potential). (Incidentally, we could also have assigned zero as the potential energy before the fall and -mgh the potential on the floor) You can therefore read equation (2) as “the potential energy of a falling small mass is converted to its kinetic energy”. Note that you can also read the equation backwards , as in “a small mass thrown in the air has its kinetic energy converted to potential energy”.
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