Suppose you have just poured a cup of freshly brewed coffee with temperature 95∘c in a room where the temperature is 25∘c. newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. therefore, the temperature of the coffee, t(t), satisfies the differential equation dtdt=k(t−troom) where troom=25 is the room temperature, and k is some constant. suppose it is known that the coffee cools at a rate of 2∘c per minute when its temperature is 65∘c. a. what is the limiting value of the temperature of the coffee? b. what is the limiting value of the rate of cooling? c. find the constant k in the differential equation. d. use euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.

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.

On a day when the barometer reads 75.23 cm, a reaction vessel holds 250 ml of ideal gas at 20 celsius. an oil manometer ( ρ= 810 kg/m^3) reads the pressure in the vessel to be 41 cm of oil and below atmospheric pressure. what volume will the gas occupy under s.t.p.?

Compare the horizontal displacement of the two balls as they travel to the ground. what do you observe?