Two protons are 1 × 10−10 m apart (about one atomic radius). Which interaction between two protons is stronger, the gravitational attraction or the electric repulsion? Note that since both the gravitational and electric forces depend on the inverse square distance, this comparison holds true at all distances, not just at a distance of 1 × 10−10 m. Use the accurate values of G = 6.67 × 10−11 N·m2/kg2, proton mass of 1.67 × 10−27 kg, and electron mass of 9.11 × 10−31 kg.

a) First, calculate the electric force |Felec| = ___ N

b) Next, calculate the gravitational force |F grav| = ___ N

c) Calculate the ratio of the two forces |Felec|/|Fgrav| = ___

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

The energy equivalent of the rest mass of an electron is

Asmall grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2 . what net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2 ?