Aradioactive substance decays according to the formula w = 20e¡kt grams where t is the time in hours. a find k given that after 50 hours the weight is 10 grams. b find the weight of radioactive substance present at: i t = 0 hours ii t = 24 hours iii t = 1 week. c how long will it take for the weight to reach 1 gram? d find the rate of radioactive decay at: i t = 100 hours ii t = 1000 hours. e show that dw dt is proportional to the weight of substance remaining.

If this plastic cup is heated to its melting point, what will eventually happen to all the particles in the plastic? a. the particles will begin to move enough that they slide past each other. b. bonds will form and the liquid will become a solid. c. the spaces between the particles will get smaller. d. the particles will change state and become a crystalline solid.

For problems 1-3, consider a simple dc brush motor with a permanent magnet stator. with an an consider a simple dc brush motor with a permanent magnet ae supply voltage of 100 v, the no-load speed of the motor is 1000 rpm. this motor can provide a torque of 1.9 n-m at 800 rpm drawing a current of 2 a current are both zero at no load.) 1. with an armature supply voltage of 100 v, the motor is operated at 900 rpm. what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input? what is the energy efficiency of the motor? with an armature supply voltage of 100 v, the motor is operated at 1100 rpm (where it acts as a generator). what torque input is required? what mechanical power is required what current is generated? what is the electrical power generated? what is the energy efficiency of the motor acting as a generator? 2. with an armature supply voltage raised to 120 v, the motor is operated at 1000 rpm. what is the no-load speed? what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input what is the energy efficiency of the motor? 3.

Two polarizers are oriented at 70∘∘ to one another. unpolarized light falls on them. what fraction of the light intensity is transmitted?