Chapter 9: Problem 4
Why is a \(10-\mathrm{m}\) fall onto concrete far more dangerous than a 10 -m fall onto water?
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Chapter 9: Problem 4
Why is a \(10-\mathrm{m}\) fall onto concrete far more dangerous than a 10 -m fall onto water?
These are the key concepts you need to understand to accurately answer the question.
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Two particles of masses \(m_{1}\) and \(m_{2}\) move uniformly in different circles of radii \(R_{1}\) and \(R_{2}\) about the origin in the \(x, y\) -plane. The coordinates of the two particles in meters are given as follows \((z=0 \text { for both). Here } t\) is in seconds: \(x_{1}(t)=4 \cos (2 t)\) \(y_{1}(t)=4 \sin (2 t)\) \(x_{2}(t)=2 \cos \left(3 t-\frac{\pi}{2}\right)\) \(y_{2}(t)=2 \sin \left(3 t-\frac{\pi}{2}\right)\) a. Find the radii of the circles of motion of both particles. b. Find the \(x\) - and \(y\) -coordinates of the center of mass. c. Decide if the center of mass moves in a circle by plotting its trajectory.
Two identical billiard balls collide. The first one is initially traveling at \((2.2 \mathrm{m} / \mathrm{s}) \hat{\mathbf{i}}-(0.4 \mathrm{m} / \mathrm{s}) \hat{\mathbf{j}}\) and the second one at \(-(1.4 \mathrm{m} / \mathrm{s}) \hat{\mathbf{i}}+(2.4 \mathrm{m} / \mathrm{s}) \hat{\mathbf{j}}\). Suppose they collide when the center of ball 1 is at the origin and the center of ball 2 is at the point \((2 R, 0)\) where \(R\) is the radius of the balls. What is the final velocity of each ball?
A proton traveling at \(3.0 \times 10^{6} \mathrm{m} / \mathrm{s}\) scatters elastically from an initially stationary alpha particle and is deflected at an angle of \(85^{\circ}\) with respect to its initial velocity. Given that the alpha particle has four times the mass of the proton, what percent of its initial kinetic energy does the proton retain after the collision?
You are coasting on your 10-kg bicycle at 15 m/s and a 5.0-g bug splatters on your helmet. The bug was initially moving at \(2.0 \mathrm{m} / \mathrm{s}\) in the same direction as you. If your mass is \(60 \mathrm{kg},\) (a) what is the initial momentum of you plus your bicycle? (b) What is the initial momentum of the bug? (c) What is your change in velocity due to the collision with the bug? (d) What would the change in velocity have been if the bug were traveling in the opposite direction?
Find the center of mass of a thin wire of mass \(m\) and length \(L\) bent in a semicircular shape. Let the origin be at the center of the semicircle and have the wire arc from the \(+x\) axis, cross the \(+y\) axis, and terminate at the \(-x\) axis.
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