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1401Lab4 - The Second Law of Motion Theory The Second Law...

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The Second Law of Motion Theory : The Second Law of Motion states that: “The acceleration of an object is directly proportional to the net force applied to the object and inversely proportional to the mass of the object.” If the acceleration is in units of meters/sec 2 , the mass is in units of kilograms, and the force is in units of Newton’s, then the second law of motion is expressed by the equation F = m a [1] In equation [1], F is the net applied force, m is the mass of the object on which the force is applied, and a is the acceleration of the object in response to the force. In this experiment, a force will be applied to a cart of mass m 1 (mass of cart plus the added mass), by hanging weights on a string which is attached over an almost frictionless pulley to the cart, as sketched in Figure 2 - 1. There is however, some friction between the cart and the track. Let F f be the force of friction which opposes the motion of the cart. The hanging weight W 2 is opposed by the force of friction on the cart, F f . Recall that the weight, W 2 , is related to the mass, m 2 , by the equation W 2 = m 2 * g , [2] Leveling Knob Stop m 1 m 2 smart pulley Figure 2 - 1
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where g is the acceleration due to gravity (about 9.8 m/s 2 ). The net force, which accelerates both the cart and the hanging mass (i.e., the total mass of the system ), is then F = ( W 2 - F f ), Hence, equation 1 may be rewritten as W 2 - F f = m a [3] W 2 = m a + F f [4] where m is the total mass of the system, i.e. m = m 1 + m 2 . Notice that Equation [4] is of the form of a straight line, y = kx + b, provided the total mass (m 1 + m 2 ) is constant as W 2 is varied. Thus, theory predicts that if the hanging weight is plotted as a function of the acceleration of the system, a straight line should result.
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