final_exam_F06_solutions

final_exam_F06_solutions - Physics 40A - Final Exam...

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Physics 40A - Final Exam Solutions - Fall 2006 Problem 1 [25 points] A box of mass 1.0 kg on a 30° frictionless incline is connected to a box of mass 3.0 kg on a horizontal frictionless surface as shown in the diagram below. The pulley is frictionless and massless. (a) If the magnitude of F is 2.3 N, what is the tension in the connecting cord? (b) What is the largest value that the magnitude of F may have without the connecting cord becoming slack? Solution: (a) We apply Newton's second law along the x -axis to the block of mass m 1 = 3.0 kg, with the x -axis pointing horizontally to the right: F T = m 1 a Next we apply Netwon's second law along the x -axis to the block on the incline of mass m 2 = 1.0 kg, with the x -axis pointing down the incline: m 2 g sin − T = m 2 a Adding the two equations above gives: m 2 g sin  F = m 1 m 2 a a = m 2 g sin  F m 1 m 2 = 1.0 kg  9.8 m/s 2 sin 30 ° 2.3 N 3.0 kg 1.0 kg a = 1.8 m/s 2 From the first equation above, we find T = m 1 a F = 3.0 kg  1.8 m/s 2 − 2.3 N T = 3.1 N (b) At the point that F reaches is maximum value causing the cord to become slack, the tension becomes zero. Therefore, Newton's second law for each block now gives: F = m 1 a m 2 g sin = m 2 a From the second equation we get a = g sin = 9.8 m/s 2 sin 30 ° = 4.9 m/s 2 Substituting into the first equation gives: F = m 1 a = 3.0 kg  4.9 m/s 2 F = 14.7 N 1
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Physics 40A - Final Exam Solutions - Fall 2006 Problem 2 [25 points] A rigid rod of length L and negligible mass has a ball with mass m attached to one end and its other end fixed, to form a pendulum (see the Figure below). The pendulum is inverted, with the rod straight up and the ball directly above the fixed point, and then released from rest. When the pendulum reaches the lowest point ( θ = 0), what are (a) the ball's speed, and (b) the tension in the rod? (c) The pendulum is next released at rest from a horizontal position. At what angle from the vertical does the tension in the rod equal the weight of the ball? Solution:
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final_exam_F06_solutions - Physics 40A - Final Exam...

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