Physics: Work. Please answer meticulously with complete solution You and your bi
ID: 1308271 • Letter: P
Question
Physics: Work. Please answer meticulously with complete solution
You and your bicycle have a combined mass M. You wish to ride up a Berkeley hill which starts at sea level (y=0) at the Bay's edge and ends at elevation y=H. The direction of the road is always due East, and thus we define the (horizontal) "+x" direction as due East. Just to be fancy, you strap a GPS (global positioning system) apparatus to your handlebars. Among other things, this device can display your horizontal velocity component vx. It turns out someone has surveyed the road and discovered that, for y between 0 and H, the road elevation is accurately given by the mathematical expression y = Cx2, with C a positive constant and x the x-axis position coordinate (the road starts at x=0, y=0). You start at the bottom of the road and, keeping an eye on the GPS, pedal at whatever rate necessary to keep the GPS indicating a constant, known, vx This means your actual speed along the roadway is probably changing, as the roadway is not in general horizontal or even at a constant angle. What total work must you do to transport yourself and your bicycle from the bottom to the top of the hill? Remember, at the bottom of the hill (y=0) you are already moving, and you are also moving at the "top" of the hill, just as you reach y=H. What is the minimum instantaneous power that your legs must be capable of to perform the hill climb as desired?Explanation / Answer
a)work done=mgH
b)instantaneous power=dW/dt
=mg*dy/dt
=2mgC*x*vx