Homework 10 Sol.

Homework 10 Sol. - Abd Elhai, Mohamed – Homework 10 –...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 &lt; . 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....
View Full Document

Homework 10 Sol. - Abd Elhai, Mohamed – Homework 10 –...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online