Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 5, Problem 23P
To determine
The point to which the centre of mass shifts when one bends over and the change in body that caused the change in the location of the centre of mass.
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The Moon is 60 Earth radii (i.e. 60 rEarth) from the center of the Earth and has a mass of 0.012 Earth masses (i.e. 0.012 mEarth)
a. How many Earth radii is the center of mass (the “barycenter”) of the Earth-Moon system from the center of the Earth?
b. Is the center of mass inside the Earth or outside the Earth?
c. What point along the line from the center of the Earth to the center of the Moon orbits the barycenter of the Solar System in a (nearly) circular orbit (e.g. the center of the Earth, the barycenter of the Earth-Moon system, the midpoint, the center of the Moon)?
1. A thin strip of metal of mass M is bent into a quarter circle with radius R. Relative to a
coordinate system where the center of the circle is at the origin, what is the position of its
center of mass, (Xem, yem)? The integrals you'll need to compute to find the center of mass are
given below. You answer should be symbolic, in terms of R (for example, 0.1R).
y
M xdm
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Chapter 5 Solutions
Physics for Scientists and Engineers
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
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- 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.)arrow_forwardTwo 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.arrow_forwardIf 1 of the Earth’s mass were transferred to the Moon, how far would the center of mass of the Earth-Moon-population system move? The mass of the Earth is 5.971024kg and that of the Moon is 7.341022kg . The radius of the Moon’s orbit is about 3.84105m .arrow_forward
- 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.arrow_forwardA 2.00-kg particle has a velocity (2.00i3.00j)m/s, and a 3.00-kg particle has a velocity (1.00i+6.00j)m/s. Find (a) the velocity of the center of mass and (b) the total momentum of the system.arrow_forwardProfessional Application Two manned satellites approaching one another, at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00103 kg, and the second a mass of 7.50103 kg (a) Calculate the final velocity (after docking) by using the frame of reference in which the first satellite was originally at rest. (b) What is the loss of kinetic energy in this inelastic collision? (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.arrow_forward
- Objects "mAmA" and "mBmB" have the same mass, and "mCmC" has double the mass of "mAmA". Which of the following locations best represents the object's center of mass? 5 3 4 1 2arrow_forwardTwo astronauts each having a mass of 75kg are connected by a 10m rope of negligible mass. They are isolated in space, orbiting thier center of mass at speeds of 5 m/s. a) By pulling on the rope, one of the astronauts shortens the distance between them to 5m. What are the astronauts mew speeds? b) By pulling on the rope, one of the astronauts shortens the distance between them to 5m. What is the new rotational energy of the system? c) By pulling on the rope, one of the astronauts shortens the distance between them to 5m. How much work is done by the astronaut in shortening the rope?arrow_forwardA spaceship with fuel is initially at rest at point CG. Fuel is ejected at the back to propel the payload to the forward direction. After a long time, the total fuel ejected out has a mass of 1e6 pounds, and center of gravity moving backward at 20 m/s. The forward speed of the payload relative to CG is 150 m/s. The payload mass is _____ pounds.arrow_forward
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