2. In an engine, a piston oscillates with simple harmonic mo- tion so that its position varies according to the expression * = (5.00 cmjons (21 + w/6) where's is in centimeters and f is in seconds. At ( = 0 find (a) the position of the piston, (b) Find the period and amplitude of the motion. 3. The position of a particle is given by the expression x = (100 m)ce(500 mi + w), where x is in meters and / is in seconds, Determine (a) the frequency and period of the motion, (b) the amplitude of the motion. (c) the phase constant, and (d) the position of the particle at / - 0.250 s. D. A wave is described by y - (200 cm) sin(kx - ed), where k = 2.11 rad/m, or = 3.62 rad/s, x is in meters, and f is in second. Determine the amplitude, wavelength, frequency, and speed of the wave. A segment of steel railroad track has a length of 30:000 m when the temperature h 0.0"C. (A) What is its length when the temperature is $0.0"C? An ideal gas occupies a volume of 100 em" at 20'G and 100 Pa. Find the number of moles of gas in the container, A certain scuba tank is designed to hold 66.0 [ of air when it is at atmospheric pressure at 22' C. When this volume of air is compressed to an absolute pressure of 3000 1b/in. and stored in a 10,0-1. (0.350-03) tank, the air becomes so hot that the tank must be allowed to cool before it can be ted, Before the air cools, what is its temperature? (Assume that the air behaves like an ideal gas.) How much energy is required to change a 40.0-g ice cube from ice at - 10.0'C to steam at 1 10"(7 A beam of light of wavelength 550 nm traveling in air is inci- dent on a slab of transparent material. The incident beam makes an angle of 40.0" with the normal, and the refracted beam makes an angle of 26.0" with the normal. Find the index of refraction of the material. A light may of wavelength 589 am traveling through air is incident on a smooth, flat slab of crown glass at an angle of $0.0' to the normal, as sketched in Figure $5.15. Find the angle of refraction. Find the critical angle for an air-water boundary. (The index of refraction of water is 1.53.) The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.5 X 10-" m. Find the magnitudes of the electric force and the gravitational force between the two particles. Consider three point charges located at the corner of a right triangle as shown in Figure 21.8, where q - g - 50 AC. 47 - -20 AC, and a = 0.10m. Find the force on q3 due to ql and q2 (ii) Calculate the electric potential energy of the system. (iii) Find the electric potential at the origin of the system. (iv) Find individual electric field in between q2 and q3 due to charges