Because g varies so little over the extent of most structures, any structure's center of gravity effectively coincides with its center of mass. Here is a fictitious example where g varies more significantly. The figure shows an array of six particles, each with mass m, fixed to the edge of a rigid structure of negligible mass. The distance between adjacent particles along the edge is 1.00 m. Following are the values of g at each particle's location: Particle 1: g = 7.96 m/s² 7.76 m/s2 Particle 3: g = 7.54 m/s? = 7.40 m/s? Particle 5: g = 7.54 m/s² 7.76 m/s? Particle 2: g Particle 4: g Particle 6: g Using the coordinate system shown, find (a) the x coordinate xcom and (b) the y coordinate ycom of the center of mass of the six- particle system. Then find (c) the x coordinate xcog and (d) the y coordinate ycog of the center of gravity of the six-particle system. 6. (a) Number Units (b) Number Units (c) Number Units

Because g varies so little over the extent of most structures, any structure's center of gravity effectively coincides with its center of mass. Here is a fictitious example where g varies more significantly. The figure shows an array of six particles, each with mass m, fixed to the edge of a rigid structure of negligible mass. The distance between adjacent particles along the edge is 1.00 m. Following are the values of g at each particle's location: Particle 1: g = 7.96 m/s² 7.76 m/s2 Particle 3: g = 7.54 m/s? = 7.40 m/s? Particle 5: g = 7.54 m/s² 7.76 m/s? Particle 2: g Particle 4: g Particle 6: g Using the coordinate system shown, find (a) the x coordinate xcom and (b) the y coordinate ycom of the center of mass of the six- particle system. Then find (c) the x coordinate xcog and (d) the y coordinate ycog of the center of gravity of the six-particle system. 6. (a) Number Units (b) Number Units (c) Number Units

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 9.59P: Figure P9.59a shows an overhead view of the configuration of two pucks of mass In on frictionless...

See similar textbooks

Similar questions

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?
An astronaut out on a spacewalk to construct a new section of the International Space Station walks with a constant velocity of 2.00 m/s on a flat sheet of metal placed on a flat, frictionless, horizontal honeycomb surface linking the two parts of the station. The mass of the astronaut is 75.0 kg, and the mass of the sheet of metal is 245 kg. a. What is the velocity of the metal sheet relative to the honeycomb surface? b. What is the speed of the astronaut relative to the honeycomb surface?
The space shuttle uses its thrusters with an exhaust velocity of 4440 m/s. The shuttle is initially at rest in space and accelerates to a final speed of 1.00 km/s. a. What percentage of the initial mass of the shuttle (including the full fuel tank) must be ejected to reach that speed? b. If the mass of the shuttle and fuel is initially 1.85 106 kg, how much fuel is expelled?
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 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?
Check Your Understanding Suppose we included the sun in the system. Approximately where would the center of mass of the Earth-moon-sun system be located? (Feel free to actually calculate it.)
Find the center of mass of a cone of uniform density that has a radius R at the base, height h, and mass M. Let the origin be at the center of the base of the cone and have +z going through the cone vertex.
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 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.
A ball of mass 250 g is thrown with an initial velocity of 25 m/s at an angle of 30 with the horizontal direction. Ignore air resistance. What is the momentum of the ball after 0.2 s? (Do this problem by finding the components of the momentum first, and then constructing the magnitude and direction of the momentum vector from the components.)
In an experiment designed to determine the velocity of a bullet fired by a certain gun, a wooden block of mass M = 500.0 g is supported only by its edges, and a bullet of mass m = 8.00 g is fired vertically upward into the block from close range below. After the bullet embeds itself in the block, the block and the bullet are measured to rise to a maximum height of 25.0 cm above the blocks original position. What is the speed of the bullet just before impact?
Each Voyager spacecraft was accelerated toward escape speed from the Sun by the gravitational force exerted by Jupiter on the spacecraft. (a) Is the gravitational force a conservative or a nonconservative force? (b) Does the interaction of the spacecraft with Jupiter meet the definition of an elastic collision? (c) How could the space-craft be moving faster after the collision?