Galileo dropped two cannonballs, a large one and a small one, from the Leaning Tower of Pisa. They were both made of solid iron, but the large one (L) had a diameter twice as large as the small one (S). Both balls started from rest, and they hit the ground at the same time. Which of the following statements correctly describe the situation? Choose all that apply. More than one answer may be correct. O The Earth must have pulled harder on the smaller cannonball because it had less inertia. O The Earth pulled on the two cannonballs equally hard. O The two cannonballs fell with the same acceleration. O The Earth must have pulled harder on the larger cannonball because it had more inertia. O The two cannonballs had the same amount of inertia.

Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) 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 level.

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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)?

Grab a meter stick or any uniform thin piece of wood about 1m in length. (e.g. the handle of a broom with the head removed). Place your index fingers at either end so that you are holding the stick up with just two fingers. Move your fingers slowly together. Where do they end up? Describe the motion of your fingers. Explain why this happens.

There are numerous moons around the planet Saturn. During the formation of our solar system, these astronomical bodies would have interacted and possibly collided with each other. Imagine that one moon of mass m1 and circular orbital radius r1 originally had a velocity v1 until it collided with another moon of mass m2. This collision caused moon m1 to move in a new circular orbit with velocity 1.25v1. What is the new radius of m1 moon’s orbit?