____Master. Error corrected on problem 7 on 20 Apr/98
Please look at the screen for a list of useful constants and conversions factors.
You may leave your answers in unrationalized form. eg E = weight * height Joules. There is no need to use a calculator to multiply out the numbers. The quantities must be in a consistent set of units. The preferred units are the International units….. m, sec, joules and watts. Answers with mixed units will be marked-off.
| question | possible points | points |
| 1 | 10 | |
| 2 | 20 | |
| 3 | 10 | |
| 4 | 10 | |
| 5 | 30 | |
| 6 | 20 | |
| 7 | 20 | |
| 8 | 10 | |
| total | 130 |
1. Similarity analysis.
A 3 man shell should be how much faster than a one man shell
If the one man shell is able to complete a head race in 20 minutes, how long would the 3 man shell take for the same course... assuming that the similarity analysis is valid.
The speed of shells varies as n^(1/9). This means that the 3 man shell is faster than the two man shell by 3^(1/9).
The time to complete the race is consequently reduced since t = d/v and d is the same. t'/t = v/v' = 1/ 3^(1/9)
Or time = 20min/3^(1/9) = 20/1.13 = 17.7 minutes.
2. Speed of response.
a)Suppose a certain individual is able to react with his foot to a stimulus to his ears within 0.2 seconds. The recorded times between the gun and the first pressure on the foot plates of sprinters is found to be 0.1 second. How can the foot plate response be so fast? Please explain this.
The response time is limited by the transmission time of the nerve signal which propagates rather slowly. If one can use a nerve which is shorter, the response time will consequently be shorter. In the case of the sprinter, he can activate the hip flexor to begin the run because the hip flexors have a much shorter path to the brain.
b)Please outline how some of the ancient martial arts techniques utilize the shortest travel time of the nerve response in order to react quickly to a new situation.
In order to react quickly to your opponent, you must, of course, must sense your opponent's move. You can shorten your reaction time if you use the muscles which have shorter nerve pathways. These will be the ones which are close to your head and usually close to your trunk.
3. Two riders will propel a tandem bike faster than a one rider bike. What is the physics reason for this?
When riding fast, the main power you consume is the power loss caused by the air resistance. The faster you ride, the more power you lose to air resistance. The fastest you can ride if when the power loss to the air is balanced by the input power to the pedals. For tandem riders, the air resistance is almost the same as the resistance of one rider. The doubling of the input power to the pedals produces a new balance at a higher speed.
4. Will two linked jumpers be able to jump twice as high? Explain the reason for this [Assume that the linkage does not interfere with the motion of the jumpers.]
In this case, the power to jump to a certain height for two jumpers is just twice the power needed for one jumper. Having two jumpers linked together gives twice the power but it also requires twice the power to reach the same height. There is no gain in height for two jumpers.
5. A 70 Kg athlete consumes 7000 Kcalories per day of food. Assuming that the person is maintaining a stable weight.
a) Where does the energy from the food go?
The energy is burnt up by the athlete in work done in motion and in body heat. [Part of the motion is the motion of the internal organs to breathe and pump blood, etc.]
b)What is the average power of work [averaged over one-day] that the athlete can do? [assume 20% of total power can be put to work.] Express your answer in watts.
The total power averaged per day is P = 143 *7000/3000 = 334 watts. If only 20% is available for mechanical work, then the average power is Pwork = 0.2 * 334 = 67 watts.
c) How much power for rowing can this person generate in a 5 minute interval assuming [20% of the total power is the work output]? Express this in watts.
For a 5 minute interval, the rower can obtain about 10X more power than the average power output. This would be
P(5 minutes) = 10* 67 = 670 watts.
6. Running Stairs.
If your maximum power output permits you to run a 2.7 meter height of stairs in 2 seconds.
a) Estimate your minimum time for the stair climb if you were to carry a person (piggy back) up the stairs who weighs the same as you do. [In this question, assume that you have enough total energy but the limiting factor is your maximum power output.]
The addition of more weight would increase the energy necessary to go up the stairs by x2. Since power is the same and P=E/t.
t = E/P. t'/t = E'/E = 2. Or t' = 4 seconds.
b)Estimate the minimum time if the person being carried had half your weight?
In this case, the energy required is increased by 1.5. so t'/t = 1.5 and t' = 3 seconds.
7.Assume that an able 70 kg athlete can output 350 watts for a period of 7 minutes.
a)How high can she climb up a hill during the 7 minute period?
E = P*t = weight * height. Height = P*t/weight = 350 *7*60/700 = 210 m.
b) How many Kcalories of food can she expend during this time?
Recall that the 350 watts is the mechanical energy output for the climbing. This is only 20% of what the body burns. The total power is 5*350 watts = 1750 watts.
The total output energy is P*t = 350 *5* 7 *60 Joules. In food energy, this is converted using 1 Kcalorie = 4132 Joules.
Total Energy = P*t*1 Kilocalorie/4132 J = 350*5*7*60/4132 = 180 Kilocalories… Not Much for weight loss.
8. While the fastest part of the body for a rare athlete can move at close to 100 mi/hr, an ordinary person can use his body with a modest effort to use the bow and arrow to propel the arrow at 140 mi/hr. The power during the propulsion of the arrow is larger than the body can produce. Explain how this is consistent with the principle that energy is conserved [the principle that you don't get something for nothing.]
While the output power of the arms and shoulders are rather modest, the total energy produced is enough to produce the kinetic energy of a 140 mi/hr arrow. The power requirement is high for propelling the arrow. The high power for a short time is obtained by the spring of the bow and string and not by your body. Energy is conserved and not power. You put the energy into the bow and string and get it out in a short time. In sports motion, this is often used to advantage in martial arts and in raquet sports.