Include units please Because g varies so little over the extent of most structures, any structure's center of gravity effectively coincides with its center ofmass. Here is a fictitious example where g varies more significantly. The figure shows an array of six particles, each with mass m, fixedto the edge of a rigid structure of negligible mass. The distance between adjacent particles along the edge is 1.40 m. Following are thevalues of g at each particle's location:Particle 1: g 7.94 m/s²Particle 2: g 7.87 m/s²Particle 3: g = 7.67 m/s²Particle 4: g 7.48 m/s²Particle 5: g = 7.67 m/s²Particle 6: g 7.87 m/s²Using the coordinate system shown, find (a) the x coordinate Xcom and (b) the y coordinate ycom of the center of mass of the six-particlesystem. Then find (c) the x coordinate Xcog and (d) the y coordinate y cog of the center of gravity of the six-particle system.36SUPPORT

the center of mass of a six-particle system.Finding the Center of Mass (COM):The center of mass…

Answered: Because g varies so little over the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter11: Collisions

Section: Chapter Questions

Problem 28PQ

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A particle has a momentum of magnitude 40.0 kg m/s and a kinetic energy of 3.40 102 J. a. What is the mass of the particle? b. What is the speed of the particle?
A comet is traveling through space with speed 3.33 104 m/s when it encounters an asteroid that was at rest. The comet and the asteroid stick together, becoming a single object with a single velocity. If the mass of the comet is 1.11 1014 kg and the mass of the asteroid is 6.66 1020 kg, what is the final velocity of their combination?
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 particle of mass m moving along the x-axis with a velocity component +u collides head-on and sticks to a particle of mass m/3 moving along the x-axis with the velocity component −u. What is the mass M of the resulting particle?
In a laboratory experiment, an electron with a kinetic energy of 50.5 keV is shot toward another electron initially at rest (Fig. P11.50). (1 eV = 1.602 1019 J) The collision is elastic. The initially moving electron is deflected by the collision. a. Is it possible for the initially stationary electron to remain at rest after the collision? Explain. b. The initially moving electron is detected at an angle of 40.0 from its original path. What is the speed of each electron after the collision? FIGURE P11.50
A model rocket is shot straight up and explodes at the top of its trajectory into three pieces as viewed from above and shown in Figure P10.44. The masses of the three pieces are mA = 100.0 g, mB = 20.0 g, and mC = 30.0 g. Immediately after the explosion, piece A is traveling at 1.50 m/s, and piece B is traveling at 7.00 m/s in a direction 30 below the negative x axis as shown. What is the velocity of piece C? FIGURE P10.44 Problems 44 and 45. 45. We can use the conservation of momentum (Eq. 10.9). The total initial momentum is zero, so the sum of all the final momenta should be zero. mAvAf+mBvBf+mCvCf=0 This velocities for A and B can be expressed as vectors. vAf=1.50jm/svBf=(7.00im/s)cos30(7.00jm/s)sin30=(6.06i3.50j)m/s We can now solve the momentum equation. (100.0g)(1.50jm/s)+(20.0g)(6.06i3.50j)m/s+(30.0g)vCf=0vCf=(4.04i2.67j)m/s The velocity of piece C is down and to the right as expected.
One object (m1 = 0.200 kg) is moving to the right with a speed of 2.00 m/s when it is struck from behind by another object (m2 = 0.300 kg) that is moving to the right at 6.00 m/s. If friction is negligible and the collision between these objects is elastic, find the final velocity of each.
A cart filled with sand rolls at a speed of 1.0 m/s along a horizontal path without friction. A ball of mass m = 2.0 kg is thrown with a horizontal velocity of 8.0 m/s toward the cart as shown in Figure P11.79. The ball gets stuck in the sand. What is the velocity of the cart after the ball strikes it? The mass of the cart is 15 kg. FIGURE P11.79 Problems 79 and 80.
A ball of mass 50.0 g is dropped from a height of 10.0 m. It rebounds after losing 75% of its kinetic energy during the collision process. If the collision with the ground took 0.010 s, find the magnitude of the impulse experienced by 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?
A bullet of mass m = 8.00 g is fired into and embeds itself in a large 1.50-kg block of wood, initially at rest. What was the original speed of the bullet if that block with the embedded bullet were moving at a speed of 1.10 m/s immediately after the collision?
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?

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