Answers to Questions.
last update on 29 May, 1997
Questions.
1. If wings of a certain dimension can support a 700kg airplane flying at 60m/s, what is the relative area of the hydrofoils [underwater wings] to support a boat of 700 kg at the same speed. What is the relative wing area to support the same boat at 25 m/s .
The dynamic pressure to create lift varies as A*r, the area x the density of the medium. If this product is to remain constant, the area for the hydrofoil must be 1000 times smaller than the wing for air.
2. If a cyclist can produce a sustained 300 watts output, he can propel a bike at 17m/s. If he is to be able to propel the bike at 25m/s, how much power output must he reach?
Since power varies as v^3. The ratio of power's is (25/17)^3 = 3.1. The cyclist must produce 954 watts to maintain the speed of 25m/s.
3. If our 300 watt cyclist can propel a bike at 17m/s , and you were to put him into an underwater man-powered submarine, what speed can he sustain? Please show the reason for this.
Since Power varies as r*v^3, we have that v varies as (power/r)^(1/3). Since the powers are equal and the r ratio is 1/1000, the underwater velocity is 10 times less or 1.7m/s.
4. In the Greek Legend, Daedelus was able to fly with wings that were about 2 meters by 1/2m. The modern Daedelus flew with a wing that was much ,much larger [wingspan bigger than a 737]. What is the physics behind this? Comparethe power required to fly with a 2m wing compared to a wing with a span of 30m. [estimate the speed of flight]. Is human powered flight possible with a 2m wingspan? or a 2 m helicopter?
To produce suffienct lift with a small wing, we must have high dynamic pressures which means high velocities. This means that a lot of kinetic energy is put into the air. The human power flights have all been with very large wings with craft that fly at about 6 m/s. The large wing craft puts a large mass of air into motion with a small velocity hence a much smaller kinetic energy. The rate of kinetic energy going into the air has to be less than 300 watts for a human powered plane to work. The legendary Daedelus with small wings cannot sustain flight because of the limitation of human power. This prohibition is the same for the 2m helicopter which must also put a small mass of fluid into large speed motion.
5. Use the graphs from the tennis section and answer the following questions. These should help you to decide upon your tennis strategy if you combine these probabilities with the laws of probability.
a) What is the ratio of angular acceptance for a fair service for a ball with no spin and with topspin at 90mph and hit from a height of 105 inches.
The graph of angular acceptance shows that the 90mph serve from 105" ht is 1.5deg for a spinless ball and about 3 degrees for the topspine ball. This eans that ratio of angular acceptances is 2. You would increase your chance of getting ball into play by a factor of 2.
b)What is the ratio of angular acceptance for a ball with topsin hit at 90mph for 105inches and 85 inches.
The ratio is 3/2 in favour of the higher service.
c) What is the ratio of angular acceptances for a ball hit with topspin at a height of 105 inches at 70mph compared to 110mph?
The ratio of acceptance is 3.5/2.5 in favour of the slower service.
6. Please use figure 12, p 92 in Brancazio's basketball article to answer this question. You should not regard the sketches of the ball's path in figures 3,4,7,8 very seriously, they are just for illustrative purposes. If you are to sketch a shot launched at 50 degrees it appears to have a much lower trajectory than what Brancazio has illustrated.
a) What is the best launch angle and the angular acceptance of making a clean shot when the velocity is 22.4ft/sec?
The angle of launch varies from 47 to 53 degrees and the middle and best launch angle would be 50 degrees.
b)What is the best launch angle and the angular acceptance of making a clean shot when the velocity is 23 ft/sec?
The angle of launch for a clean shot varies from 56 to 59 degrees so that the acceptance is only 3 degrees which is 2 times less than the shot fired with the smaller velocity.
c) For a shot launched at 60 degrees, what is the range of speeds to make a clean shot?
The range of speeds is 23.2 to 23.5 ft/s, a rather small window.
d) For a shot launched at 50 degrees, what is the range of speeds to make a clean shot?
The range of speeds is 22.4 to 22.6 ft/sec.
7. If a truck needs 200HP to travel at 60 mph in air, how much power does a submarine [of a smilar size] need to travel at the same speed underwater?
Since power required varies as r, the density of the medium, the submarine must have 1000 times more power to travel at 60 mph or 200,000 HP!!!
8. A major league fastball is perceived to be rising from an otherwise straight trajectory. Is this so in objective reality? How much does a Randy Johnson change its height and in which direction from the original line of delivery?
While the fast ball is perceived to be rising from a straight line, the reality is that ball rises by only a few inches from the 40" drop from gravity.