b. In Case A, a ball is released from rest at the top of a frictionless hill of height h. In Case B, anidentical ball is released from rest at the top of a hill of height h with sufficient friction that theball can roll without slipping. In which case does the center of mass of the ball have a largerspeed at the bottom of the hill or is it the same in both cases? Explain.

Answered: Image /qna-images/answer/cc1f3ab4-006f-4579-9287-c04740367836.jpg

Answered: b. In Case A, a ball is released from…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 12PQ

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Two metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each individual meterstick is at its midpoint, and the mass of each meterstick is m. a. Where is the center of mass of the two-stick system as depicted in the figure, with the origin located at the intersection of the sticks? b. Can the two-stick system be balanced on the end of your finger so that it remains lying flat in front of you in the orientation shown? Why or why not? FIGURE P10.18 (a) The center of mass of the stick on the x axis would be at (0.5 m, 0), and the center of mass of the stick on the stick on the y axis be at (0, 0.5 m), assuming the sticks are uniform. We can then use Equation 10.3 to find the x and y coordinates of the center of mass. xCM=1Mj=1nmjxj=12m[m(0.50m)]=0.25myCM=1Mj=1nmjyj=12m[m(0.50m)]=0.25m The location of the center of mass is (0.25m,0.25m) (b) No. The location of the center of mass is not located on the object, so your finger would not be in contact with the object. In a different orientation, balancing by applying a force at the center of mass might be possible, but not in the orientation shown.
All three disks are made of sheet metal of the same material, and the diameters are 1.3 m , 2.6 m , and 3.9 m . Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right.Assume that the x-axis has its origin at the left-most point of the left-most object and it points to the right. a.Determine the location of the center of mass of the system s Express your answer with the appropriate units. B.Repeat the calculation for three solid spheres all made of the same metal and having the same diameters as in part A.
1.A fireworks rocket is launched vertically into the night sky with an initial speed of 44.2 m/s. The rocket coasts afterbeing launched, then explodes and breaks into two pieces of equal mass 2.50 s later. (a) If each piece follows a trajectory that is initially at 45.0° to the vertical, what was their speed immediately after the explosion? (b) What is the velocity of the rocket’s center of mass before and after the explosion? (c) What is the acceleration of the rocket’s center of mass before and after the explosion?Explain and labled the drawing.
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A lamina has the shape of a triangle with vertices at (−2,0), (2,0), and (0,7). Its density is ρ=2 A. What is the total mass? B. What is the moment about the x-axis? C. What is the moment about the y-axis? D. Where is the center of mass? (__,___)
A small ball of mass 0.50 kg is attached by a massless string to a vertical rod that is spinning as shown below. When the rod has an angular velocity of 6.0 rad/s, the string makes an angle of 30° with respect to the vertical. (a) If the angular velocity is increased to 10.0 rad/s, what is the new angle of the string? (b) Calculate the initial and final angular momenta of the ball. (c) Can the rod spin fast enough so that the ball is horizontal?
A Ball Rolling Uphill. A bowling ball rolls without slipping up a ramp that slopes upward at an angle b to the horizontal .Treat the ball as a uniform solid sphere, ignoring the finger holes. (a) Draw the free-body diagram for the ball.Explain why the friction force must be directed uphill. (b) What isthe acceleration of the center of mass of the ball? (c) What minimumcoefficient of static friction is needed to prevent slipping?
A meter stick has a center of mass at the 50 cm mark. Using two fingers, one at the 20 cm mark and the other at the 30 cm mark, you hold the meter stick in a horizontal, stationary position. Given the force at the 20 cm mark is 2 N, find the mass of the meter stick.
In the figure below, three thin, uniform bars of length L form a U inverted. Each vertical bar has a mass m, while the vertical bar has a mass M = 2m. What are the x and y coordinates of the center of mass of the system?
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We watch two identical astronomical bodies A and B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation is Ri. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this twobody system. Use the principle of conservation of mechanical energy (Kf + Uf = Ki + Ui) to find the following when the centerto- center separation is 0.5Ri : (a) the total kinetic energy of the system, (b) the kinetic energy of each body, (c) the speed of each body relative to us, and (d) the speed of body B relative to body A. Next assume that we are in a reference frame attached to body A (we ride on the body). Now we see body B fall from rest toward us. From this reference frame, again use Kf + Uf = Ki + Ui to find the following when the center-to-center separation is 0.5Ri : (e) the kinetic energy of body B and (f) the speed of body B relative to body A. (g) Why…

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