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alnasser (fha246) - Homework 06 - erskine - (55695) This print-out should have 16 questions. Multiple-choice questions may continue on the next...
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# How can I solve questions 7 &amp; 9 in the attached file?

alnasser (fha246) – Homework 06 – erskine – (55695) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices before answering. 001 10.0 points The suspended m 1 mass on the right is moving up, the m 2 mass slides down the ramp, and the suspended m 3 mass on the left is moving down. There is friction between the block and the ramp, with the coe±cient of the kinetic friction μ . The acceleration of gravity is g and the acceleration of the three block system is a . The pulleys are massless and frictionless. m 2 μ θ m 3 m 1 What is the equation of motion of the three- block system? 1. m 3 g + m 2 g (1 - μ ) - m 1 g = ( m 1 + m 2 + m 3 ) a 2. m 3 g + m 2 g (sin θ - μ sin θ ) - m 1 g = ( m 1 + m 2 + m 3 ) a 3. m 3 g + m 2 g (1 - μ ) - m 1 g = ( m 1 + m 3 ) a 4. m 3 g + m 2 g (sin θ - μ cos θ ) - m 1 g = ( m 1 + m 2 + m 3 ) a 5. m 3 g + m 2 g (cos θ - μ cos θ ) - m 1 g = ( m 1 + m 2 + m 3 ) a 6. m 3 g + m 2 g (cos θ - μ cos θ ) - m 1 g = ( m 1 + m 3 ) a 7. m 3 g + m 2 g (cos θ - μ sin θ ) - m 1 g = ( m 1 + m 2 + m 3 ) a 8. m 3 g + m 2 g (sin θ - μ sin θ ) - m 1 g = ( m 1 + m 3 ) a 9. m 3 g + m 2 g (sin θ - μ cos θ ) - m 1 g = ( m 1 + m 3 ) a 10. m 3 g + m 2 g (cos θ - μ sin θ ) - m 1 g = ( m 1 + m 3 ) a 002 (part 1 of 2) 10.0 points A block is released from rest at the top of a plane inclined at an angle of 34 . The coe±- cient of kinetic friction varies along the plane according to the relation μ k = σx , where x is the distance along the plane measured in meters from the top and where σ = 0 . 2 m 1 . The acceleration of gravity is 9 . 8 m / s 2 . Determine how far the block slides before coming to rest. ( Hint: ²ind the acceleration of the block and integrate to Fnd the velocity. Note that dv dt = dv dx dx dt p Answer in units of m. 003 (part 2 of 2) 10.0 points Determine the maximum speed the block at- tains. Answer in units of m / s. 004 10.0 points Hint: This problem requires a train of logic. (1) Analyze force diagram, (2) use Newton’s Laws, and (3) solve the equations of motion. A block starts from rest at a height of 4 . 1 m on a Fxed inclined plane. The acceleration of gravity is 9 . 8 m / s 2 .
alnasser (fha246) – Homework 06 – erskine – (55695) 2 5 . 5 kg μ = 0 . 12 32 What is the speed of the block at the bot- tom of the ramp? Answer in units of m / s. 005 (part 1 of 2) 10.0 points The 8 . 3 N weight is in equilibrium under the inFuence of the three forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 6 . 8 N force acts from above on the right at an angle of 63 with the horizontal. The force 8 . 3 N acts straight down. F 6 . 8 N 8 . 3 N 63 α What is the magnitude of the force F ? Answer in units of N. 006 (part 2 of 2) 10.0 points What is the angle α of the force F as shown in the ±gure? Answer in units of . 007 10.0 points Two blocks of masses m 1 and m 2 are con- nected by a spring of force constant k and negligible mass. v F m 1 m 2 If the upper block of mass m 1 is pulled up- ward by a constant force F , by how much does the spring between masses 1 and 2 stretch (in terms of k , F , and the masses) when the blocks have the same upward acceleration? 1. m 2 m 1 F k 2. F k 3. Zero; the spring will remain unstretched since it doesn’t need to exert any force; v F does it all. 4. ( m 1 + m 2 ) F m 2 k + ( m 1 m 2 ) g 5. None of these 6. ( m 1 + m 2 ) F m 1 k + ( m 1 m 2 ) g 7. m 1 F k ( m 1 + m 2 ) + M 2 g 8. m 1 m 2 F k 9. m 2 F k ( m 1 + m 2 ) 008 10.0 points To test the performance of its tires, a car travels along a perfectly Fat (no banking) cir- cular track of radius 87 . 7 m. The car increases its speed at uniform rate of a t d | V | dt = 3 . 77 m / s 2 until the tires start to skid. If the tires start to skid when the car reaches a speed of 15 . 4 m / s, what is the coe²cient of static friction between the tires and the road? The acceleration of gravity is 9 . 8 m / s 2 .
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