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This is a generic question I’m just confused about one thing please it clear it up I attached 2 questions about the same topic of a collision between a rod and a bullet why is one always positive before and after collision And the other one is negative

This is a generic question I’m just confused about one thing please it clear it up I attached 2 questions about the same topic of a collision between a rod and a bullet why is one always positive before and after collision And the other one is negative

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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This is a generic question I’m just confused about one thing please it clear it up I attached 2 questions about the same topic of a collision between a rod and a bullet why is one always positive before and after collision And the other one is negative
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) 2 (a) Conservation of angular momentum: mv! = -mv / + I win where I = I HL² and wis the Find the angular velocity: angular velocity immediately after the collision mv 1/2 = -mv 2 + 1 ML ²1 3 2mv! 13 ML m,v ⇒3mv ML max = 3x 0.00lx 100 = 0.35 ¹ = win IxI ↓ (1-cost max) with reference to the figure, using the work-
Transcribed Image Text: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) 2 (a) Conservation of angular momentum: mv! = -mv / + I win where I = I HL² and wis the Find the angular velocity: angular velocity immediately after the collision mv 1/2 = -mv 2 + 1 ML ²1 3 2mv! 13 ML m,v ⇒3mv ML max = 3x 0.00lx 100 = 0.35 ¹ = win IxI ↓ (1-cost max) with reference to the figure, using the work-
Problem 3-Conservation of angular momentum and physical pendulum A system is composed of a thin uniform rod of length L=1m and mass M = 1 kg, and a bullet of mass mb = 7 g. Initial, the rod is in equilibrium against the force of gravity, with its axis along the vertical direction, pivoted at a distance L/4 from the rod's upper end; the bullet travels along the x-direction, with initial velocity v = 100 m/s, until it collides against the rod at a distance L/4 from the rod's lower end. After the collision, the bullet emerges from the rod with a velocity v' = 50 m/s along the x-direction, and the rod starts rotating around its pivot point. (a) Find the initial angular velocity of the rod. (6) Use conservation of energy to find the maximum angle reached by rod. (c) Find the time it takes for the rod to return to its original position, in the limit where the maximum angle reached by the rod is small (Hint: in part b, use 1- cos a = 2 (sin a/2)² ). (a) conservation of angular momentam: myvh=myw'h + Iowa m where h=L/2 is the distance between the pivot point and the point of contact of the bullet with the rod and I is the moment of inertia of the rod with respect to the pivot point. I₁ = I₁N+M(+)² = 1 m² + m² = 7 Me ² H
Transcribed Image Text:Problem 3-Conservation of angular momentum and physical pendulum A system is composed of a thin uniform rod of length L=1m and mass M = 1 kg, and a bullet of mass mb = 7 g. Initial, the rod is in equilibrium against the force of gravity, with its axis along the vertical direction, pivoted at a distance L/4 from the rod's upper end; the bullet travels along the x-direction, with initial velocity v = 100 m/s, until it collides against the rod at a distance L/4 from the rod's lower end. After the collision, the bullet emerges from the rod with a velocity v' = 50 m/s along the x-direction, and the rod starts rotating around its pivot point. (a) Find the initial angular velocity of the rod. (6) Use conservation of energy to find the maximum angle reached by rod. (c) Find the time it takes for the rod to return to its original position, in the limit where the maximum angle reached by the rod is small (Hint: in part b, use 1- cos a = 2 (sin a/2)² ). (a) conservation of angular momentam: myvh=myw'h + Iowa m where h=L/2 is the distance between the pivot point and the point of contact of the bullet with the rod and I is the moment of inertia of the rod with respect to the pivot point. I₁ = I₁N+M(+)² = 1 m² + m² = 7 Me ² H
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