Two objects are connected by a light string that passes over a frictionless pull

Question

Two objects are connected by a light string that passes over a frictionless pulley as shown. The incline is frictionless and the masses are m1 = 5.00 kg, m2 = 3.00 kg, and ? = 40.0 degrees. Find the magnitude of the acceleration of m2 (absolute value), to within 5%. The units of the answer should be in m/s2.

Explanation / Answer

(a) Let T = tension in the string and a = common acceleration. => 6 * 9.8 * sin 55° - T = 6a and T - 2 * 9.8 * sin 55° = 2a Adding, 4 * 9.8 * sin 55° = 8a => a = 4.9 sin 55° = 4.01 m/s^2 (b) T = 2a + 2 * 9.8 * sin 55° = 2 * 4.01 + 19.6 * sin 55° = 24.07 N (c) v = at = 4.01 * 2 = 8.02 m/s. If the angle is 35° to the horizontal, answers will be (a) 2.81 m/s^2 (b) 16.9 N (c) 5.62 m/s

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