Problem Set 5

Reading for this past week was Chapter 7 sections 1-7. Reading for this coming week is Chapter 7 sections 8-10 and Chapter 8. It is best to read the material before class (say, over the weekend) and re-read it afterwards. The following problems are due Wednesday October 10 at 4 PM.

(1) Explain the mistake the editors made at the NYT in 1920:

"As a method of sending a missile to the higher, and even to the highest parts of the earth's atmospheric envelope, Professor Goddard's rocket is a practicable and therefore promising device. It is when one considers the multiple-charge rocket as a traveler to the moon that one begins to doubt ...for after the rocket quits our air and really starts on its journey, its flight would be neither accelerated nor maintained by the explosion of the charges it then might have left. Professor Goddard, with his ``chair'' in Clark College and countenancing of the Smithsonian Institution, does not know the relation of action to re-action, and of the need to have something better than a vacuum against which to react ...Of course he only seems to lack the knowledge ladled out daily in high schools."

--- New York Times Editorial, 1920

(2) Ch 6 P 72 Designers of today’s cars have built “5 mph (~ 8 km/h) bumpers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h. If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is tested by ramming into a solid wall?

(3) Ch 7 P 18 You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50 km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. (b) Calculate the average deceleration of the car.

(4) Car designers also build cars that crumple on impact. Why has this helped reduce fatalities in auto accidents?

(5) Ch 6 P 54 A skier traveling 12.0 m/s reaches the foot of a steady upward 18.0º incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?

(6) Ch 7 P 4 A child in a boat throws a 6.40-kg package out horizontally with a speed of 10.0 m/s, Fig. 7–31. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance.

(7) Ch 7 P 29 A cube slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? Assume that both leave the incline moving horizontally and that the incline does not move.

(8) Ch 7 P 42 Billiard ball A of mass 0.400 kg moving with speed 1.80 m/s strikes ball B, initially at rest, of mass 0.500 kg. As a result of the collision, ball A is deflected off at an angle of 30.0º with a speed 1.10 m/s. (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the velocity of ball B. Do not assume the collision is elastic.

(9) Find an application of conservation of energy or momentum that is not on this problem set. Write a brief description including a statement of the application and the use of a conservation law. Both whimsical and serious applications are welcome.

(10) The annnual total energy consumption in the Unitied States is about 9.76 X 10^(19) J [2004 data from the International Atomic Energy Agency (IAEA)]. (a) What is the average rate of consumption in Watts? (b) If the population is 291 million, what is the average rate electrical consumption per person? What is the energy consumed per person? (c) Sunlight transfers approximately 1.0 kW per square meter by radiation (or what we call "light"). If this energy could be collected at an efficiency of 40%, how large an area would be required to collect the energy used by the US? Compare area this to the area of your home state. (d) Compare the US data to that of Ireland: 5.99 X 10^(17) J with a population of 4 million.