Answered: solve and draw the center of mass of…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter10: Systems Of Particles And Conservation Of Momentum

Section: Chapter Questions

Problem 20PQ

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Center of Mass Revisited N Find the center of mass of a system with three particles of masses 1.0 kg, 2.0 kg, and 3.0 kg kept at the vertices of an equilateral triangle of side 1.0 m (Fig. P10.15). FIGURE P10.15
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.
A bomb, initially at rest, explodes into several pieces. (a) Is linear momentum of the system (the bomb before the explosion, the pieces after the explosion) conserved? Explain. (b) Is kinetic energy of the system conserved? Explain.
Figure 8.16 shows a cube at rest and a small object heading toward it. (a) Describe the directions (angle 1 ) at which the small object can emerge after colliding elastically with the cube. How does 1 depend on b, the so-called impact parameter? Ignore any effects that might be due to rotation after the collision, and assume that the cube is much more massive than the small object. (b) Answer the same questions if the small object instead collides with a massive sphere. Figure 8.16 A small object approaches a collision with a much more massive cube, after which its velocity has the direction 1. The angles at which the small object can be scattered are determined by the shape of the object it strikes and the impact parameter b.
Two particles of masses m1 and m2 move uniformly in different circles of radii R1 and R1 about the origin in the x, y-plane. The coordinates of the two particles in meters are given as follows ( z=0 for both). Here t is in seconds: x1(t)=4cos(2t) y1(t)=4sin(2t) x2(t)=2cos(3t2) y2(t)=2sin(3t2) 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.
The figure below shows a bullet of mass 200 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. a. What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact? b. What is the magnitude and direction of the impulse by the block on the bullet? c. What is the magnitude and direction of the impulse from the bullet on the block? d. If it took 3 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?
A baseball bat of uniform denisty is cut at the location of its center of mass as shown in Figure 8.17. Which piece has the smaller mass? (a) the piece on the right (b) the piece on the left (c) both pieces have the same mass (d) impossible to determine Figure 8.17 (Quick Quiz 8.5) A baseball bat cut at the location of its center of mass.
Two particles of masses m1 and m2 separated by a horizontal distance D are let go from the same height h at different times. Particle 1 starts at t=0 , and particle 2 is let go at t=T . Find the vertical position of the center of mass at a time before the first particle strikes the ground. Assume no air resistance.
A uniform piece of sheet metal is shaped as shown in Figure P9.24. Compute the x and y coordinates of the center of mass of the piece. Figure P9.24
A bomb, initially at rest, explodes into several pieces. (a) Is linear momentum of the system (the bomb before the explosion, the pieces after the explosion) conserved? Explain. (b) Is kinetic energy of the system conserved? Explain.
Professional Application Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. How is the motion of the center of mass affected by the explosion? How would it be affected if the pieces experienced significantly more air resistance than the intact shell?
Two particles of masses m1 and m2 , move uniformly in different circles of radii R1 and R2 R2 about origin in the x, y-plane. The x- and y-coordinates of the center of mass and that of particle 1 are given as follows (where length is in meters and tin seconds): x1(t)=4cos(2t) , y1(t)=4sin(2t) and: xCM(t)=4cos(2t) , yCM(t)=3sin(2t) . a. Find the radius of the circle in which particle 1 moves. b. Find the x- and y-coordinates of particle 2 and the radius of the circle this particle moves.

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solve and draw the center of mass of the point masses m1=15kg,m2=20kg, m3=50kg x1=5m, x2=8m, x3=6m