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Unformatted text preview: Abd Elhai, Mohamed – Homework 10 – Due: Apr 22 2008, 9:00 pm – Inst: Dr Kevin Dean 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. This is ONLINE HOMEWORK No. 10 It is due by 06:00 AM Abu Dhabi Time on Tuesday 22 April (9:00 PM Monday 21 April, Texas time). 001 (part 1 of 3) 5 points A solid sphere of radius R and mass M is held against a wall by a string being pulled at an angle θ . f is the magnitude of the frictional force and W = M g . W P F θ R To what doesthe torqueequation X i ~ τ i = 0 about point O (the center of the sphere) lead? 1. F = f correct 2. W = f 3. F cos 2 θ = f 4. F sin θ cos θ = f 5. F + W = f 6. F sin θ = f Explanation: W P F θ R R f Applying rotational equilibrium about O , the center of the sphere, X i ~ τ i = 0i, so τ c = τ cc F R = f R F = f . 002 (part 2 of 3) 5 points To what does the vertical component of the force equation lead? 1. F cos θ + W = f 2. F sin θ = W 3. F sin θ + f = W correct 4. F sin θ = f 5. F sin θ = f + W Explanation: Applying translational equilibrium verti- cally, X i F yi = F sin θ + f-W = 0 F sin θ + f = W . 003 (part 3 of 3) 5 points Find the smallest coefficient of friction μ needed for the wall to keep the sphere from slipping. 1. μ = sin θ 2. μ = cos θ Abd Elhai, Mohamed – Homework 10 – Due: Apr 22 2008, 9:00 pm – Inst: Dr Kevin Dean 2 3. μ = 1 cos θ correct 4. μ = 1 tan θ 5. μ = 1 sin θ 6. μ = tan θ Explanation: Let N be the normal force. f ≤ μN ; when μ is minimal, f = μN . Applying transla- tional equilibrium horizontally, X i F xi = F cos θ- N = 0 = μN cos θ- N = 0 = N ( μ cos θ- 1) = 0 μ = 1 cos θ . keywords: rotational equilibrium, transla- tional equilibrium 004 (part 1 of 1) 5 points A ladder is leaning against a smooth wall. There is friction between the ladder and the floor, which may hold the ladder in place; the ladder is stable when μ ≥ 1 2 tan θ . mg L f 45 ◦ h b F N μ = 0 . 4 The ladder will be 1. at the critical point of slipping. 2. stable. 3. unstable. correct Explanation: Stability requires μ ≥ 1 2 tan 45 ◦ = 0 . 5 . Since μ = 0 . 04 < . 5 , the ladder is unstable. keywords: static equilibrium, instability 005 (part 1 of 3) 2 points Consider a simplified model of the Golden Gate bridge, where the bridge is represented by four equal weights, each weighing 6 N , hanging from a wire. The angle between the hanging wire and the vertical supporting beam is θ = 43 ◦ (refer to the figure). The bridge is symmetric. T 1 T 2 6 N 6 N 6 N 6 N θ 43 ◦ β 90 ◦ Figure: Not drawn to scale. Calculate T 1 , the tension in the left segment of the wire....
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