11. Momentum & Impulse

For a uniform, solid baseball resting on Earth's surface, where is its $\mathrm{center of mass}$ located, and where is its $\mathrm{center of gravity}$ located?

Where is the center of mass of the $\mathrm{Earth}–\mathrm{Moon}$ system located relative to the two bodies?

Given a system of two point masses, $m_1$ located at $x_1$ and $m_2$ located at $x_2$, what is the formula for the x-coordinate $x_{\mathrm{cm}}$ of the center of mass of the system?

(II) A thin 7.0-kg wheel of radius 34 cm is a uniform disk and is weighted to one side by a 1.50-kg weight, small in size, placed 24 cm from the center of the wheel. Calculate the position of the center of mass of the weighted wheel.

For a hollow, uniformly dense soccer ball, where is the $\mathrm{center} \mathrm{of} \mathrm{mass}$ located?

Given a system of three particles with masses $m_1$, $m_2$, and $m_3$ located at positions $x_1$, $x_2$, and $x_3$ along the x-axis, which of the following expressions correctly gives the x-coordinate $x_{\mathrm{cm}}$ of the center of mass of the system?

The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 x 10⁻¹⁰ m. How far from the carbon atom is the center of mass of the molecule?

(I) The CM of an empty 1750-kg Jeep is 2.40 m behind the front of the Jeep. How far from the front of the Jeep will the CM be when two people sit in the front seat 2.80 m from the front of the Jeep, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 65.0 kg.

(II) A uniform thin wire is bent into a semicircle of radius R. Determine the coordinates of its center of mass with respect to an origin of coordinates at the center of the “full” circle.

(III) Determine the CM of a machine part that is a uniform cone of height h and radius R, Fig. 9–51. [Hint: Divide the cone into an infinite number of circular disks of thickness dz, one of which is shown.]

(III) Determine the CM of a uniform pyramid that has four triangular faces and a square base with equal sides all of length s. [Hint: See Problem 63.]

(II) A 52-kg woman and a 72-kg man stand 8.6 m apart on nearly frictionless ice. How far from the woman is their cm?

Find the center of mass of the ammonia molecule. The chemical formula is NH₃. The hydrogens are at the corners of an equilateral triangle (with sides 0.16 nm) that forms the base of a pyramid, with nitrogen at the apex (0.037 nm vertically above the plane of the triangle).

The masses of the Earth and Moon are 5.98 x 10²⁴ kg and 7.35 x 10²² kg, respectively, and their centers are separated by 3.84 x 10⁸ m. Where is the CM of the Earth–Moon system located?

A huge balloon and its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed v, measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?