Answer Key to 2009 Test 1

Answer Key to 2009 Test 1 - w1 1=Mg wx w1 =Mg1 =Mg N y1 N N...

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30 o M m w 1 =Mg N T 1 f s a 1 =0 w 2 =mg T 2 a 2 =0 w 1 =Mg N T 1 f k a 1 w 2 =mg T 2 a 2 x 1 y 1 x 2 y 2 30 o w 1 w y w x 30 o w 1 =Mg N T 1 a 1 w 2 =mg T 2 a 2 =0 Towards the hole 45° 45° #1 #2 #3 #4 P R Q Answers PHYS116A.01 Midterm Exam 1 Version 2 (Version 1 answers are a permutation of Version 2 answers) Problem 1 At the top of an inclined plane that is at a 30 o angle with the horizontal, there is a frictionless pulley. Two wooden blocks, one of mass M= 1 kg that lies on the plane and another of mass m=0.30 kg that hangs from the pulley are connected with a thin massless string. Initially the blocks are not moving. Then at t=0 we push the first block so that it gets velocity v 0 =0.5 m/s upwards along the plane. The coefficient of kinetic friction between the block and the plane is μ k =0.2 . Assume that the string is long enough and the ground far enough, so that the second block never reaches the pulley or the ground while the first block lies on the inclined plane. ( sin(30 o ) = 1/2, cos(30 o ) = /2 ) Show your work! 1. Draw the free body diagrams of the two blocks before they start moving 2. Draw the free body diagrams of the two blocks after they start moving
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3. The static friction force before the blocks start moving is We choose coordinate systems as follows (the components of w 1 are shown): This value is positive. If we have started with the f s pointing in the negative direction, we would get a negative value, which will tell us that f s is pointing in the opposite. a. f s = M g cos(30 o ) + m g b. f s = M g + m g sin(30 o ) c. f s = M g cos(30 o ) - m g d. *** f s = M g sin(30 o ) - m g e. f s = M g sin(30 o ) + m g 4. The minimal coefficient of static friction μ s , for the blocks to stay at rest is a. 0.41 b. 0.12 c. 0.32 d. 0.39 e. *** 0.23 5. After the blocks start moving, their acceleration (if the positive direction along the plane is upwards) is:
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This is the component a x of along the positive x 1 axis. Its numerical value is negative, which means that is pointing in the negative x 1 direction as shown on the free body diagram. (Note, that the magnitude of a is (Mg( sin 30 o + μ k cos 30 o
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Answer Key to 2009 Test 1 - w1 1=Mg wx w1 =Mg1 =Mg N y1 N N...

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