Question

For this problem, use equation (6) on page 15 except that T_A is now variable. ( dT/dt = k(T-T_A)

A warehouse is built without the capacity for heating or cooling. There are two insulation options. One will give the warehouse a time constant of 2 hour (k=1/2), while the second will give a time constant of 7 hours (k=1/7).

The outside temperature follows a sine wave given below:

TemperatureC) = 24 – 7 cos(π t/12) – 4 sin(π t/12)

where time (t) is given in 24 hour military.

At t=0, the temperature inside the warehouse is 16C

Write out the differential equation for each time constant, and determine what the temperature will be inside the ware house at 8:00 (day 1), 12:00 (day 2), and 20:00 (day 3) for each insulation package.

Over the long term, describe the temperature inside the warehouse.

A cannon ball weighs 10kg. It is shot vertically into the air at a speed of 100 m/s. Assuming no air resistance, how high will the cannon ball go? Now assume an air resistance coefficient of k=0.0025. Now compute the maximum height of the cannon ball and its velocity when it strikes the ground. Model for terminal velocity assuming the drag coefficient is proportional to velocity. (as per my lecture material)

Answer 1