Homework #7 - Inclines -solutions

Homework #7 - Inclines -solutions - sanchez(es25396...

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sanchez (es25396) – Homework #7 - Inclines – guevara – (130101) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A block accelerates 3 m / s 2 down a plane in- clined at angle 27.0 . The acceleration of gravity is 9 . 81 m / s 2 . m μ k 3 m / s 2 27 Find μ k between the block and the inclined plane. 1. 0.166 correct 2. 0.853 3. 1.289 4. 0.510 5. 0.148 Explanation: Given : a = 3 m / s 2 , θ = 27 , and g = 9 . 81 m / s 2 . Consider the free body diagram for the block m g sin θ N = m g cos θ μ N a m g Basic Concepts: vector F net = mvectora Parallel to the ramp: F x,net = ma x = F g,x - F k F g,x = mg sin θ F k = μ k F n Perpendicular to the ramp: F y,net = F n - F g,y = 0 F g,y = mg cos θ Solution: Consider the forces parallel to the ramp: F k = F g,x - ma x = mg sin θ - ma x Consider the forces perpendicular to the ramp: F n = F g,y = mg cos θ Thus the coefficient of friction is μ k = F k F n = m g sin θ - m a m g cos θ = g sin θ - a g cos θ = 9 . 81 m / s 2 sin 27 - 3 m / s 2 9 . 81 m / s 2 cos 27 = 0 . 166306 . 002 10.0 points A block sits motionless on an inclined plane, held in place by friction. The plane could be tilted even more upwards and the block would remain motionless. M μ s θ
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sanchez (es25396) – Homework #7 - Inclines – guevara – (130101) 2 Consider the following statements: I. The magnitude of the frictional force equals M g sin θ . II. The magnitude of the frictional force is less than M g sin θ . III. The magnitude of the frictional force is greater than μ s M g sin θ . IV. Static friction must vanish since the block is not moving. V. The magnitude of the frictional force equals μ s M g cos θ . VI. The magnitude of the frictional force is less than μ s M g cos θ . Select the appropriate answer below. Caution: You must consider all 6 statements above carefully. 1. Only II and IV are true. 2. Only IV is true. 3. Only VI is true. 4. Only VI and II are true. 5. Only V and III are true. 6. Only V is true. 7. Only I and VI are true. correct 8. Only III is true. 9. Only I is true. 10. Only II is true. Explanation: Consider the free body diagram for the block M g sin θ N = M g cos θ F f M g Basic Concept summationdisplay F = M a . Call the direction parallel to the incline x and that perpendicular to it y . Since the block is not moving, then we know the forces must add to zero in any particular direction. Also, the force pulling back on the block is the component of the weight along that direction, W x = m g sin θ . Then, the force of friction must be equal to the com- ponent of the weight in the x direction, so, F f = m g sin θ .
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