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Unformatted text preview: alexander (jra2623) – oldhomework 11 – Turner – (92510) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points The suspended 2 . 3 kg mass on the right is moving up, the 1 . 3 kg mass slides down the ramp, and the suspended 8 . 4 kg mass on the left is moving down. The coefficient of friction between the block and the ramp is 0 . 17 . The acceleration of gravity is 9 . 8 m / s 2 . The pulleys are massless and frictionless. 1 . 3 k g μ = . 1 7 24 ◦ 8 . 4 kg 2 . 3 kg What is the acceleration of the three block system? Correct answer: 5 . 24861 m / s 2 . Explanation: Let : m 1 = 2 . 3 kg , m 2 = 1 . 3 kg , m 3 = 8 . 4 kg , and θ = 24 ◦ . Basic Concept: F net = ma negationslash = 0 Solution: The acceleration a of each mass is the same, but the tensions in the two strings will be different. Let T 1 be the tension in the right string and T 3 the tension in the left string. Consider the free body diagrams for each mass T 3 m 3 g a T 1 m 1 g a T 3 T 1 N μ N a m 2 g For the mass m 1 , T 1 acts up and the weight m 1 g acts down, with the acceleration a di rected upward F net 1 = m 1 a = T 1 − m 1 g (1) For the mass on the table, the parallel compo nent of its weight is mg sin θ and the perpen dicular component of its weight is mg cos θ . ( N = mg cos θ from equilibrium). The accel eration a is directed down the table, T 3 and the parallel weight component m 2 g sin θ act down the table, and T 1 and the frictional force μ N = μ m 2 g cos θ act up the table F net 2 = m 2 a (2) = T 3 + m 2 g sin θ − T 1 − μ m 2 g cos θ . For the mass m 3 , T 3 acts up and the weight m 3 g acts down, with the acceleration a di rected downward F net 3 = m 3 a = m 3 g − T 3 . (3) Adding Eqs. (1), (2), & (3) yields ( m 1 + m 2 + m 3 ) a = m 3 g + m 2 g sin θ − μ m 2 g cos θ − m 1 g . Solving for a , we have a = [ m 2 sin θ − μ m 2 cos θ + ( m 3 − m 1 )] g m 1 + m 2 + m 3 = (1 . 3 kg) (9 . 8 m / s 2 ) sin 24 ◦ 2 . 3 kg + 1 . 3 kg + 8 . 4 kg − (0 . 17) (1 . 3 kg) (9 . 8 m / s 2 ) cos 24 ◦ 2 . 3 kg + 1 . 3 kg + 8 . 4 kg + (8 . 4 kg − 2 . 3 kg) (9 . 8 m / s 2 ) 2 . 3 kg + 1 . 3 kg + 8 . 4 kg = 5 . 24861 m / s 2 . alexander (jra2623) – oldhomework 11 – Turner – (92510) 2 002 (part 2 of 3) 10.0 points(part 2 of 3) 10....
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This note was uploaded on 10/20/2011 for the course PHY 302K taught by Professor Kaplunovsky during the Summer '08 term at University of Texas.
 Summer '08
 Kaplunovsky
 Mass, Work

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