Linear Motion,

1. The mass of the Earth is 5.98 ✕ 1024 kg, and the mass of the Moon is 7.36 ✕ 1022 kg. The distance of separation, measured

between their centers, is 3.84 ✕ 108 m. Locate the center of mass of the Earth-Moon system as measured from the center

of the Earth.

2. Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown in the figure below.

The monument is made from tens of thousands of small stone blocks of density 3 752 kg/m3. The monument is 14.6 m

high and 61.9 m wide at its base and is everywhere 3.90 m thick from front to back. Before the monument was built many

years ago, all the stone blocks lay on the ground. How much work did laborers do on the blocks to put them in position

while building the entire monument? Note: The gravitational potential energy of an object-Earth system is given by Ug =

MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference


3. A uniform piece of sheet metal is shaped as shown in the figure below. Compute the x and y coordinates of the center of

mass of the piece.

x = 11.7 cm

y = 13.3 cm


4. A rod of length 20.50 cm has linear density (mass per length) given by

where x is the distance from one end, and λ is measured in grams/meter.

5. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (figure). The angle between the two

bonds is 106°. If the bonds are long, where is the center of mass of the molecule? (Use a coordinate

system centered in the oxygen atom, with the x axis to the right and the y axis upward.)

6. Consider the following distribution of objects: a 4.00-kg object with its center of gravity at (0, 0) m, a 5.20-kg object at

(0, 3.00) m, and a 4.40-kg object at (4.00, 0) m. Where should a fourth object of mass 7.00 kg be placed so that the

center of gravity of the four-object arrangement will be at (0, 0)?

7. A circular pizza of radius R has a circular piece of radius R/2 removed from one side as shown in the figure below. The

center of gravity has moved from C to C’ along the x axis. Show that the distance from C to C’ is R/6. Assume the

thickness and density of the pizza are uniform throughout.

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