PHY 113, Summer 2007
Langenbrunner
HW 1 – due Thursday, May 24
(Please do the problems on a different sheet of paper. Write your name, the date, and the homework number on top of the sheet. Please show all steps, and mark your answer clearly.)
Measurement & Error
1. Use only the appropriate number of significant figures in each of the following problems.
2. The fastest growing plant on record is a Hesperoyucca whipplei that grew 3.7 m in 14 days. What was its growth rate in
a) micrometers per second?
b) fathoms per fortnight?
3. The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer (usually 43 to 53 cm). If ancient drawings indicate that a cylindrical pillar in a tomb was to have the length 9 cubits, what would have been the length in
a) meters?
b) millimeters?
c) If the diameter of the pillar was to be 2 cubits, what would have been the volume of the pillar in cubic meters?
4. The seven subspecies of marine iguana that live on the various islands of the Galapagos have been evolving independently of each other every since the first iguanas came there from the mainland about 5 million years ago (actually, that number is highly debated... but assume it for this problem). Assuming iguanas reproduce at an average age of six years, how many generations of marine iguanas have evolved on the islands?
5. I have an avocado tree that, upon last measurement, was 2 feet, 5 inches tall. What is the percent uncertainty of that measurement?
6. The equation below, when completed, is a standard one in Einstein's Theory of General Relativity. The missing quantities are r, G, and M. The units of c are meters per second (m/s), the unit of M is the kilogram (kg), the unit of r is meters (m), and the units of G are Newtons times meters squared per kilogram squared (N*m2/kg2) (N is a complex unit that is equivalent to kg*m/s2). Using dimensional analysis, fill in the equation with the missing quantities.
7. During a total solar eclipse, your view of the Sun is almost exactly replaced by your view of the moon. Assuming that the distance from you to the Sun is about 400 times the distance from you to the Moon, find the ratio of
a) the Sun's diameter to the Moon's diameter.
b) the Sun's volume to the Moon's volume.
8. The full Moon subtends the same angle that the nail of your pinky finger does when you hold your hand out at arm's length. From this information, the aid of a ruler, and the given Earth – Moon distance (find it in your book), estimate the Moon's diameter.
9. If q1 = 82.0° ± 0.5° and q2 = 8.2° ± 0.5°, what is the percent uncertainty of
a) q1?
b) q2?
c) sin(q1)?
d) sin(q2)?
(be careful with the numbers on this one...)
One Dimensional Kinematics
10. a) Can an object have zero velocity and still be accelerating?
b) Can an object have a constant velocity and still have a varying speed?
Give an example if yes, explain why if no.
11. The wings on a stonefly do not flap, and thus the insect cannot fly. However, when the insect is on a water surface, it can sail across the surface by lifting its wings into a breeze. Suppose that you time stoneflies as they move at constant speed along a straight path of a certain length. On average, the trips each take 7.1 seconds with the wings set as sails and 25.0 seconds with the wings tucked in.
a) What is the ratio of the sailing speed vs to the nonsailing speed vns?
b) In terms of vs, what is the difference in the times the insects take to travel the first 2.0 m along the path with and without sailing?
12. On the drive from Cincinnati to Rochester, I am traveling at 60 mph, 3 seconds behind a big truck in front of me (that is, the front of my car passes the same point in the road 3 seconds after the truck clears it). The trucker suddenly spots a dead deer in the road, and he swerves just in time. Unfortunately, I am "boxed in" and cannot swerve without hitting another car, so my only chance is to slam on my brakes. Can I stop in time? (Assume a truck length of 20 m, a reaction time of 400 ms, and an average deceleration of 5.18 m/s2.)
13. A graph of x versus t for a particle in straight-line motion is shown below.
a) What is the average velocity of the particle between t = 0.50 s and t = 4.5 s?
b) What is the instantaneous velocity of the particle at t = 4.5 s?
c) What is the average acceleration of the particle between 0.50 s and t = 4.5 s?
d) What is the instantaneous acceleration of the particle at t = 4.5 s?
14. In 1889, at Jubbulpore, India, a tug-of-war was finally won after 2 h 41 min, with the winning team displacing the center of the rope 3.7 m. In centimeters per minute, what was the magnitude of the average velocity of that center point during the contest?
15. Sketch a v(t) graph that would be associated with the a(t) graph shown below.
(First, redraw the curve below, taking care to label axes. You are encouraged to draw both a(t) and v(t) curves on the same graph – but if you do, make sure you label each curve separately.)
16. As the picture below shows, Clara jumped from a bridge, followed closely by Jim. How long did Jim wait after Clara jumped? Assume that Jim is 170 cm tall and that the jumping-off level is at the top of the figure.
17. An enraged Rachael drops Ross' belongings one by one out of their apartment window (15 m high). One second after she drops a open box of random items (books and rocks on the bottom, soft cottony sheets on the top), she spots Ross himself, standing open-mouthed, on the ground below, and she angrily throws the next item – a very delicate and important dinosaur bone – straight down. Much to her dismay and much to his delight, the bone softly lands right in the box just as the box hits the ground, preventing paleontological disaster.
a) How long was Ross' shriek? (Assume he shrieked for the entire length of the bone's fall.)
b) What initial speed did Rachael impart on the dino bone?
c) How fast was the bone moving right before it landed in the box?
d) Now redo the problem and switch your choice of positive direction (but keep your choice of origin). Make sure the answers are consistent.