Physics! Please help!?
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06-19-2014, 09:58 AM
Post: #1
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Physics! Please help!?
Two boxes connected by a light horizontal rope are on a horizontal surface, as shown in the following figure. The coefficient of kinetic friction between each box and the surface is 0.30. One box (box B) has mass 4.76kg , and the other box (box A) has mass m . A force F with magnitude 40.1N and direction 53.1∘ above the horizontal is applied to the 4.76kg box, and both boxes move to the right with 1.50m/s2.
A.)What is the tension T in the rope that connects the boxes? Express your answer to two significant figures and include the appropriate units. B.)What is the mass m of the second box? Express your answer to two significant figures and include the appropriate units. Ads |
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06-19-2014, 09:59 AM
Post: #2
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"as shown in the following figure" ??
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06-19-2014, 10:10 AM
Post: #3
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The setup seems clear enough.
A) B normal force Fn = mg - FsinΘ = 4.76kg * 9.8m/s² - 40.1N * sin53.1º Fn = 14.6 N so its friction force Fb = µ*Fn = 0.3 * 14.6N = 4.4 N The horizontal (accelerating) component of the applied force is Fh = 40.1N * cos53.1º = 24 N The net force horizontally is Fnet = ma = Fh - Fb - Fa where Fa is A's friction force. (4.76kg + m) * 1.50m/s² = 24N - 4.4N - 0.3 * m * 9.8m/s² Dropping units for ease (m is in kg): 7.14 + 1.5m = 19.7 - 2.94m 4.44m = 12.56 m = 2.83 kg ↠(B) tension T = Fnet + Fa = 2.83kg * 1.5m/s² + 0.3 * 2.83kg * 9.8m/s² T = 12.6 N ↠(A) Could have found tension without finding the mass of A through the fbd for B: Fnet = Fh - Fb - T 4.76kg * 1.5m/s² = 24N - 4.4N - T T = 12.5 N √ |
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