Physics lab 4 - Objective The dependence of the centripetal...

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Objective: The dependence of the centripetal force on mass, radius, and angular velocity were studied by rotating masses in horizontal circular paths at constant angular velocities. Introduction Uniform circular motion is the motion of an object in a circle at a constant speed. As the object continues with this motion it’s constantly changing direction (not speed), and is therefore accelerating. According to Newton’s second law ( F r = m a r ), an accelerating object must be acted upon by a force, in the same direction as the acceleration. The force that is required to cause this horizontal circular path is “centripetal force.” Centripetal force is constant in magnitude, never changing direction, and is perpendicular to the object’s velocity. It is also dependent on the mass and the radius of the circular motion and on the square of the angular velocity. In this experiment we will test the dependency.
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F r = m a r ……………………………….……1 According to Newton’s Second law of motion, in the radial direction, we find that the value of the centripetal force ( F r ), causing the centripetal acceleration is directly proportional to the radial inward acceleration ( a r ¿ and mass (m) of the object. a r = v 2 r = r ω 2 …………………………………..2 The radial inward acceleration ( a r ¿ acts towards the center of the circular path and causes a change in the direction of the velocity vector. Therefore, the radial inward acceleration is equal to the radius of the circular motion (r) multiplied by the angular velocity ( ω 2 ). However, if the force were to no longer exist than the object would take off in a straight line path tangent to path of circular motion. Therefore, the radial inward acceleration is also equal to the tangential velocity ( v 2 ) divided by the radius of the circular motion. F r = mrω 2 ………………………………………3 By combining equations 1 and 2, the net force ( F r ) will become equal to the radius of the circular motion (r) multiplied by the angular velocity ( ω 2 ). ω = 2 π T …………………………………………….4 For the circular motion, the circumference is equal to 2 πr . Therefore, the angular velocity ( ω 2 ) is equal to 2 π divided by the period of the circular motion (T). F r = F spring =Mg……………………………………5 The only force acting on the centripetal force ( F r ) is the force of the spring ( F spring ¿ . The spring is hanging, therefore, the only force acting on it its weight (Mg), which is the M (mass of the hanging mass multiplied by gravity. From this we can conclude that the centripetal force is equal to the force of the spring and equal to the weight of the hanging mass (Mg).
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