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Applications

# Applications - Applications Sample Problem 5-7 Figure 5.6...

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Applications Sample Problem 5-7 Figure 5.6 shows a block of mass m = 15 kg hanging from three cords. What are the tensions in these cords ? The mass m experiences a gravitational force equal to mg. Since the mass is at rest, cord C must provide an opposing force equal to mg. Applying Newton's third law, we conclude that cord C exerts a force on the knot whose magnitude is equal to mg (and pointed in the direction shown in Figure 5.6). Since the system is at rest, the net force on the knot must be equal to zero: This vector equation can be rewritten in terms of its components along the x-axis and y-axis, using the following information: Figure 5.6. Sample Problem 5-7. Using these expressions we can write down the equations for the x and y-components of the net force: The first expression can be used to express T A in terms of T B : Substituting this expression into the equation for [Sigma]F y we obtain: from which we can calculate T B : Knowing T B , we can now calculate T A :

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In the case of sample problem 5-6, the tensions in the cords are: T A = 100 N T B = 140 N T C = 150 N Problem Figure 5.7 shows a block with mass m on a frictionless plane, tilted by an angle [theta]. What is the acceleration of the block ? Figure 5.7. Mass m on an inclined plane. In order to determine the acceleration of the block we have to determine the total force acting on the block along the inclined plane. Two forces act on the block: the gravitational force exerted by the earth on the block, and a force, called the normal force exerted by the plane on the block (see Figure 5.8). This force must be present since in its absence mass m will experience free fall
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