Starting at the top of a steep, icy track, a rider jumps onto a sled (known as a

Question

Starting at the top of a steep, icy track, a rider jumps onto a sled (known as a skeleton) and proceeds - belly down and head first - to slide down the track. The track has thirteen turns and drops 97 m in elevation from top to bottom. (a) In the absence of non-conservative forces, such as friction and air resistance, what would be the speed of a rider at the bottom of the track? Assume that the speed of the rider at the beginning of the run is relatively small and can be ignored. (b) In reality, the rider reaches the bottom with a speed of 38 m/s. How much work is done on a 95-kg rider and skeleton by non-conservative forces? Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by a top rider (m = 82.0 kg) is 6.40 W per kilogram of his body mass, (a) How much work does the rider do during a 176-km race in which his average speed is 12.3 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 4186 joule = 1 nutritional Calorie. You are trying to lose weight by working out on a rowing machine. Each time you pull the rowing bar (which simulates the "oars") toward you, it moves a distance of 3.2 ft in a time of 1.6 s. The readout on the display indicates that the average power you are producing is 98 ft-lb/s. What is the magnitude of the force that you exert on the handle?

Explanation / Answer

7)

a) As there are are no Non-cnservative forces the total mechanical energy of the system is consrved.

final kinetic energy = initial potential energy

(12/)*m*v^2 = m*g*h

v = sqrt(2*g*h)

= sqrt(2*9.8*97)

= 43.6 m/s

b) Workdone by Non-conservative forces = change in mechanical energy

= (1/2)*m*v^2 - m*g*h

= (1/2)*95*38^2 - 95*9.8*97

= -2.17*10^4 J

8)

a) time taken, t = d/v

= 176*10^3/12.3

= 14309 s

Workdone = Power*time taken

= 82*6.4*14309

= 7.51*10^6 J

b) W = 7.51*10^6/4186

= 1794 nutritional cal

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