A metal wire is bent to the shape of a circular arc. The wire is shown in blue in the figure. 6. 4 2 -1 -2 -3 -5 -6 -7 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x (cm) The arc is centered around the origin. What is the x coordinate of the arc's center of the mass? Please, notice that the circular arc goes through grid intersection points. Submit Answer Incorrect. Tries 2/10 Previous Tries y (cm)

A metal wire is bent to the shape of a circular arc. The wire is shown in blue in the figure. 6. 4 2 -1 -2 -3 -5 -6 -7 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x (cm) The arc is centered around the origin. What is the x coordinate of the arc's center of the mass? Please, notice that the circular arc goes through grid intersection points. Submit Answer Incorrect. Tries 2/10 Previous Tries y (cm)

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 43PQ: A 44.0-kg child finds himself trapped on the surface of a frozen lake, 10.0 m from the shore. The...

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A 57.0-g tennis ball is traveling straight at a player at 21.0 m/s. The player volleys the ball straight back at 25.0 m/s. If the ball remains in contact with the racket for 0.060 s, what average force acts on the ball? (a) 22.6 N (b) 32.5 N (c) 43.7 N (d) 72.1 N (e) 102 N
A 0.0250-kg bullet is accelerated from rest to a speed of 550 m/s in a 3.00-kg rifle. The pain of the rifle's kick is much worse if you hold the gun loosely a few centimeters from your shoulder rather than holding it tightly against your shoulder. (a) Calculate the recoil velocity of the rifle if it is held loosely away from the shoulder. (b) How much kinetic energy does the rifle gain? (c) What is the recoil velocity if the rifle is held tightly against the shoulder, making the effective mass 28.0 kg? (d) How much kinetic energy is transferred to the rifle shoulder combination? The pain is related to the amount of kinetic energy, which is significantly less in this latter situation. (e) Calculate the momentum of a 110-kg football player running at 8.00 m/s. Compare the player's momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s. Discuss its relationship to this problem.
This is a symbolic version of Problem 23. A girl of mass mG is standing on a plank of mass mp. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vGP to the right relative to the plank. (The subscript GP denotes the girl relative to plank.) (a) What is the velocity vPI of the plank relative to the surface of the ice? (b) What is the girls velocity vGI relative to the ice surface?
A 44.0-kg child finds himself trapped on the surface of a frozen lake, 10.0 m from the shore. The child slips with each step on the frictionless ice and remains the same distance from the shoreline. Egged on by his parents, he throws a 0.750-kg ball he is carrying toward the center of the lake with a horizontal speed of 1.50 m/s, in the direction opposite that of the shoreline. a. Does the act of throwing the ball cause the child to move? If so, what are the speed and the direction of his motion with respect to the Earth? b. What are the forces acting on the child when he throws the ball?
Figure P9.59a shows an overhead view of the configuration of two pucks of mass In on frictionless ice. The pucks are tied together with a string of length 1' and negligible mass. At time t = 0, a constant force of magnitude F begins to pull to the right on the center point of the string. At time t, the moving pucks strike each other and stick together. At this time, the force has moved through a distance 4 and the pucks have attained a speed v (Fig. P9.59b). (a) What is v in terms of F, d, e, and in? (b) How much of the energy transferred into the system by work done by the force has been transformed to internal energy?
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.
Two pucks in a laboratory are placed on an air table (Fig. P11.66). Puck 2 has four times the mass of puck 1 (m2 = 4m1). Initially, puck 1s speed is three times puck 2s speed (v1i = 3v2i), puck 1s position is r1i=x1ii, and puck 2s position is r2i=y2ij. The pucks collide at the origin. a. Copy Figure P11.66 and then add vCM to your sketch. b. Does puck 2 travel a greater distance, lesser distance, or the same distance as puck 1? c. Find an expression for y2i in terms of x1i. d. If puck 1 moves 1.33 m, how far does puck 2 move before the collision? FIGURE P11.66 Problems the origin.
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?
A model rocket engine has an average thrust of 5.26 N. It has an initial mass of 25.5 g, which includes fuel mass of 12.7 g. The duration of its burn is 1.90 s. (a) What is the average exhaust speed of the engine? (b) This engine is placed in a rocket body of mass 53.5 g. What is the final velocity of the rocket if it were to be fired from rest in outer space by an astronaut on a space-walk? Assume the fuel burns at a constant rate.
Review. Two identical hard spheres, each of mass m and radius r, are released from rest in otherwise empty space with their centers separated by the distance R. They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [Gm3(1/2r 1/R)1/2. (b) What If? Find the magnitude of the impulse each receives during their contact if they collide elastically.
Your physical education teacher throws a baseball to you at a certain speed and you catch it. The teacher is next going to throw you a medicine ball whose mass is ten times the mass of the baseball. You are given the following choices: You can have the medicine ball thrown with (a) the same speed as the baseball, (b) the same momentum, or (c) the same kinetic energy. Rank these choices from easiest to hardest to catch.
Four objects are situated along the y axis as follows: a 1.86kg object is at +2.78m, a 1.11kg object is at +1.80m, a 1.40kg object is at the origin, and a 3.81kg object is at –0.55m. What is the y-coordinate of the center of mass? State your answer to two decimal places in m.