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two masses on inclined plane
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Two masses: m1 = 1.65kg and m2 = 3.3kg attached by a massless rod parallel to the incline on which both sides travel down along the plane with m1 trailing m2. The angle of incline is 30 degrees. The coefficient of kinetic friction between m1 and the incline is 0.226 ; that between m2 and the incline is 0.113.(a)... 顯示更多 Two masses: m1 = 1.65kg and m2 = 3.3kg attached by a massless rod parallel to the incline on which both sides travel down along the plane with m1 trailing m2. The angle of incline is 30 degrees. The coefficient of kinetic friction between m1 and the incline is 0.226 ; that between m2 and the incline is 0.113. (a) Find the tension in the rod linking m1 and m2. (b) Find the common acceleration of the two masses. (c) Would the answers to (a) and (b) be changed if m2 trails m1 ?
最佳解答:
(a) Let T be the tension in the rod and a be the common acceleration, then taking g = 10 m/s2, we have: Friction acting on m1 = 0.226 x 1.65 x 10 cos 30 = 3.23 N Friction acting on m2 = 0.113 x 3.3 x 10 cos 30 = 3.23 N Since m1 is trailing m2, T is pulling m1 down the slope while m2 upward. Hence: Net force acting on m1 = T + 1.65 x 10 sin 30 - 3.23 = T + 5.02 Net force acting on m2 = 3.3 x 10 sin 30 - 3.23 - T = 12.8 - T So, T + 5.02 = 1.65a ... (1) 12.8 - T = 3.3a ... (2) Adding: 17.3 = 4.95a a = 3.5 m/s2 (b) Using either (1) or (2) in (a), we can find out that T = 1.24 N (c) If m2 is trailing m1, T would change from tension to compressive force of the rod while its magnitude remains constant.
其他解答:4E350C6F8B48ECA2
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