PHYS172-F18-Exam3-PRACTICE-Final-SOLUTIONS.pdf

0 finding each of these torques separately finding

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= 0 Finding each of these torques separately: Finding 𝜏⃗ 𝑇 : Direction of 𝜏⃗ 𝐹 is clockwise −?̂ . Magnitude |𝜏⃗ 𝐹 | = ?(4?/5) Finding 𝜏⃗ ?? : Direction of 𝜏⃗ ?? is counterclockwise +?̂ . Magnitude |𝜏⃗ ?? | = (?𝑔) ( ? 2 ) Substitute in 𝜏⃗ 𝐹 + 𝜏⃗ ?? = 0 −? ( 4? 5 ) ?̂ + (?𝑔) ( ? 2 ) ?̂ = 0 ? = 5?? 8 HOW TO TWEAK: Similar Situation. The location of where ? is applied can be changed to a different point. Problem 23: [5 points] If you let go of the rod the previous question, what is the magnitude of its angular acceleration immediately after you release it? Recall that the moment of inertia of a rod taken about its end is 𝐼 = 1 3 ?? 2 . A) 𝑔/? B) 3𝑔 /2? C) 3𝑔/? D) 𝑔/2? E) 2𝑔/3? HOW TO SOLVE : Angular Acceleration: 𝛼 ⃗ = 𝜏 ⃗⃗ ??? 𝐼 ℎ𝑖??? Let us find each separately: Net torque is due to weight of rod: 𝜏⃗ ??? = 𝜏⃗ ?? = (?𝑔) ( ? 2 ) ?̂ Mom of Inertia of rod about hinge: 𝐼 ℎ𝑖??? = 𝐼 ?? + ? ( ? 2 ) 2 𝐼 ℎ𝑖??? = 1 12 ?? 2 + ? ( ? 2 ) 2 𝐼 ℎ𝑖??? = 1 3 ?? 2 Substituting: 𝛼 ⃗ = 𝜏 ⃗⃗ ??? 𝐼 ℎ𝑖??? 𝛼 ⃗ = (??)( ? 2 ) 1 3 ?? 2 𝛼 ⃗ = 3? 2?
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PHYS 172 EXAM 3 : PRACTICE (Total Points = 200 ) FALL 2018 Problem 24: [10 points] A bullet of mass, 𝒎 = 0.03 𝑘𝑔 is fired horizontally and at a distance, 𝒅 = 0.05𝑚 above the axis of a disk of mass, ? = 10 𝑘𝑔 , radius, 𝑹 = 0.10 𝑚 . The cylinder is initially at rest and is free to rotate on a massless axle through it long axis. The bullet adheres to the cylinder surface as it hits it. The cylinder begins to rotate at an angular speed such that it completes one complete revolution in, 𝑻 = 0.209 ? after catching the bullet. What is the approximate initial speed, 𝒗 of the bullet prior to impact? A) 300 m/s B) 1000 m/s C) 2000 m/s D) 3000 m/s E) None of the above HOW TO SOLVE: Angular Momentum Principle System = Bullet + Cylinder Surroundings: Nothing 𝜏⃗ ??? ∆? = ∆? ⃗⃗ ??? = 0 ? ⃗⃗ ???,𝑖 = ? ⃗⃗ ???,? ? ⃗⃗ ??????,𝑖 + ? ⃗⃗ ???𝑖????,𝑖 = ? ⃗⃗ ???,? Finding various terms: ? ⃗⃗ ??????,𝑖 : Bullet only has translational angular mom (clockwise) ? ⃗⃗ ??????,𝑖 = −𝑚𝑣? ?̂ = −𝑚𝑣𝑑?̂ ? ⃗⃗ ???𝑖????,𝑖 = 0 : It is at rest initially ? ⃗⃗ ???,? = −𝐼 ??? 𝜔?̂ = ( 1 2 ?𝑅 2 + 𝑚𝑑 2 ) 𝜔?̂ [Note: System = cylinder + point mass at distance 𝑑 from center] ? ⃗⃗ ???,? = − ( 1 2 ?𝑅 2 + 𝑚𝑑 2 ) ( 2𝜋 𝑇 ) ?̂ So, setting up the equation: ? ⃗⃗ ??????,𝑖 + ? ⃗⃗ ???𝑖????,𝑖 = ? ⃗⃗ ???,? −𝑚𝑣𝑑?̂ = − ( 1 2 ?𝑅 2 + 𝑚𝑑 2 ) ( 2𝜋 𝑇 ) ?̂ 𝑣 = ( 1 2 ?𝑅 2 + 𝑚𝑑 2 ) ( 2𝜋 ??𝑇 ) 𝑣 = ( 1 2 (10𝑘𝑔)(0.10𝑚) 2 + (0.03𝑘𝑔)(0.05𝑚) 2 ) ( 2𝜋 (0.03??)(0.05?)(0.209?) ) 𝑣 = 1152 𝑚/? ≈ 1000 𝑚/? HOW TO TWEAK: The problem can be reversed. You may be given the speed of the bullet and asked to find the angular speed of the disk after the collision.
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PHYS 172 EXAM 3 : PRACTICE (Total Points = 200 ) FALL 2018 Problem 25: [10 points] Two people with different masses sit on a see-saw that is initially are rest, ?
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