1. Some fishing line is made out of nylon with Y = 3.0 x 109 Pa and breaking stress 7.7 x107 Pa. It is 5.0 m long, you are holding one end, and it hangs down vertically.
(a) When a 3.0-kg fish is attached to the bottom end, the fishing line elongates by 1.0 cm. What is its cross sectional area? What is its diameter (assuming the cross section is circular)?
(b) What is the largest mass that can be supported by the fishing line before it breaks?
2 Three uniform spheres are fixed at the positions shown in the diagram. Assume they are completely isolated and there are no other masses nearby.
(a) What is the magnitude of the force on a 0.20 kg particle placed at the origin (Point P)? What is the direction of this force?
(b) If the 0.20 kg particle is placed at (x,y) = (-500 m, 400 m) and released from rest, what will its speed be when it reaches the origin?
(c) How much energy is required to separate the three masses so that they are very far apart?
3 (a) How far from the center of the Sun is the center of gravity of the Earth-Sun system? [Note: the radius of the Sun is 7.0 x 108 m.]
(b) Where is the point in the Earth-Sun system where the force of gravity due to these bodies on a test mass will be 0?
4 If you know the mass of a star and a planet's radius and speed at perihelion (closest approach to the star), then using conservation of energy and angular momentum you can solve for the radius and speed of that planet at aphelion (farthest point from the star).
Encke's comet has speed 7.0x104 m/s at its closest distance to the Sun (5.1x1010 m, about a third of the distance from the Earth to the Sun). What is its speed and distance from the Sun at aphelion?