In a region of space, the potential energy of the system varies with x as u = α − (βx − γ)2 , where α = 38 j, β = 1.0 j1/2m-1, γ = 17 j1/2, and x is measured in meters. a particle of mass m = 2.5 kg is initially at x0 = 11 m. assume there are no dissipative forces (friction, wind resistance, etc.) in this problem. (a) at what position is the force on the particle zero? (b) what is the potential energy of the system when the particle is at the position that you found in part (a)? is this a point of stable or unstable equilibrium?

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?

Which of the following is a characteristic shared by both electron and light microscopes? a. they both employ the use of objective lenses. b. both microscopes require an internal camera to visualize the specimen. c. both microscopes have a resolving power of 0.01 nm. d. they both utilize white light to magnify the specimen.