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Problem 2- Elastic collision between a bullet and a rod (a) A bullet with mass m and initial speed v along the horizontal direction collides elastically against a long uniform rod of length L and mass M>> m, pivotec at its upper end. The collision occurs at a distance L/2 from the rod's upper end, with the rod initially at rest with its axis along the vertical direction. Assume that L = 1m, v = 100m/s, m = 1g and M = 1kg. Estimate the maximum angle, between the vertical axis and the rod axis, reached by the rod. (Hint: use cos Omax 1-0max/2). (b) Estimate the time it takes for the rod, from the time of the initial collision with the bullet, to reach the position of maximum angle. (c) Suppose that we take the rod to a distant planet, whose mass is twice that of the Earth and whose radius is also twice that of the Earth. Estimate the 10 m/s² on Earth; in parts (b) and (c) one significant digit is enough) 2 (Hint: appro

Problem 2- Elastic collision between a bullet and a rod (a) A bullet with mass m and initial speed v along the horizontal direction collides elastically against a long uniform rod of length L and mass M>> m, pivotec at its upper end. The collision occurs at a distance L/2 from the rod's upper end, with the rod initially at rest with its axis along the vertical direction. Assume that L = 1m, v = 100m/s, m = 1g and M = 1kg. Estimate the maximum angle, between the vertical axis and the rod axis, reached by the rod. (Hint: use cos Omax 1-0max/2). (b) Estimate the time it takes for the rod, from the time of the initial collision with the bullet, to reach the position of maximum angle. (c) Suppose that we take the rod to a distant planet, whose mass is twice that of the Earth and whose radius is also twice that of the Earth. Estimate the 10 m/s² on Earth; in parts (b) and (c) one significant digit is enough) 2 (Hint: appro

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Can you explain this in steps I don’t understand what they are trying to do and I don’t get why mv after the collision becomes negative and why we are using the moment of inertia
(Hint: In points (a) and (b), Problem 2- Elastic collision between a bullet and a rod (a) A bullet with mass m and initial speed v along the horizontal direction collides elastically against a long uniform rod of length L and mass M >> m, pivoted at its upper end. The collision occurs at a distance L/2 from the rod's upper end, with the rod initially at rest with its axis along the vertical direction. Assume that L=1m, v = 100m/s, m = 1g and M = 1kg. Estimate the maximum angle, between the vertical axis and the rod axis, reached by the rod. (Hint: use cos max 10max/2). (b) Estimate the time it takes for the rod, from the time of the initial collision with the bullet, to reach the position of maximum angle. (c) Suppose that we take the rod to a distant planet, whose mass is twice that of the Earth and whose radius is also twice that of the Earth. Estimate the period of small oscillations of the rod on this distant planet? (Hint: approximate g = 10 m/s² on Earth; in parts (b) and (c) one significant digit is enough)
Transcribed Image Text:(Hint: In points (a) and (b), Problem 2- Elastic collision between a bullet and a rod (a) A bullet with mass m and initial speed v along the horizontal direction collides elastically against a long uniform rod of length L and mass M >> m, pivoted at its upper end. The collision occurs at a distance L/2 from the rod's upper end, with the rod initially at rest with its axis along the vertical direction. Assume that L=1m, v = 100m/s, m = 1g and M = 1kg. Estimate the maximum angle, between the vertical axis and the rod axis, reached by the rod. (Hint: use cos max 10max/2). (b) Estimate the time it takes for the rod, from the time of the initial collision with the bullet, to reach the position of maximum angle. (c) Suppose that we take the rod to a distant planet, whose mass is twice that of the Earth and whose radius is also twice that of the Earth. Estimate the period of small oscillations of the rod on this distant planet? (Hint: approximate g = 10 m/s² on Earth; in parts (b) and (c) one significant digit is enough)
3 / 14 Problem 2- Elastic collision, bullet and mod Conseration of angular moment gives mv √ 1²/12 = -mv = 2 + I win where I = ML²2 is the rod's moment of inertia, and Win its angular rebuity immediately after the collision. Then. mvL I The numerical value of m,v Win = = 90% + 3m V ML Win Əman ==3=/= (1-(05&max) is @₁n = 0,35! MacBook Air with W₂ = Mg = (1-cosmen and aft obtain we DIL 1-cos mex 1-cosman= = max I MgL ≈ Substituting numbers, and using gs1075/12, M we obtain 1m 3x10m 2 W₁ x = 150 3g Finally, using cos@max ~ 1 - 1 Omer, oblan 9x10²5-²-3x10³ 6x 10 → max 0,08 rad With reference to the figure, using the work- (b) The period of small oscillations of energy principle in the form Wg = = = [ (W = W²3) the rod is T= शा -2- I Mgh we 217)
Transcribed Image Text:3 / 14 Problem 2- Elastic collision, bullet and mod Conseration of angular moment gives mv √ 1²/12 = -mv = 2 + I win where I = ML²2 is the rod's moment of inertia, and Win its angular rebuity immediately after the collision. Then. mvL I The numerical value of m,v Win = = 90% + 3m V ML Win Əman ==3=/= (1-(05&max) is @₁n = 0,35! MacBook Air with W₂ = Mg = (1-cosmen and aft obtain we DIL 1-cos mex 1-cosman= = max I MgL ≈ Substituting numbers, and using gs1075/12, M we obtain 1m 3x10m 2 W₁ x = 150 3g Finally, using cos@max ~ 1 - 1 Omer, oblan 9x10²5-²-3x10³ 6x 10 → max 0,08 rad With reference to the figure, using the work- (b) The period of small oscillations of energy principle in the form Wg = = = [ (W = W²3) the rod is T= शा -2- I Mgh we 217)
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