# Homework Help: Show by dimensional analysis

1. Sep 23, 2004

### Faiza

Hi I am currently enrolled in PHY138Y1 and I need some major help in some homework questions.I'm a first TIME physics student and I have no idea what I'm doing. I attempted these questions, but I still dont comprehend what the question is asking for. There are some questions that I am having difficulty with. If you have any ways to help me figure it out that would be great!
-Faiza Khan

Q1. The position of a particle is when moving under uniform acceleration is somefunction of the elapsed time and the acceleration. Suppose we write this position as x=kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m=1 and n=2.
Can this analysis give the value of k?

Q2. At the time of a book’s printing, the U.S. national debt is
about $6 trillion. (a) If payments were made at the rate$1000 per second, how many years would it take to pay off the debt, assuming no interest were charged?

(b) A dollar bill is about 15.5 cm long. If six trillion dollar bills were laid end to end around the earth’s equator, how many times would they encircle the earth? Take the radius of the earth at the equator to be 6 378 km.

Q3. A pirate had buried his treasure on an island with five trees, located at the following points: (30 m, -20 m), (6 m, 8 m), (-10 m, -10m), (40 m, -30m), and (-70 m, 60m), all measured relative to some origin. His ship’s log instructs you to start at tree A and move toward tree B, but to cover only one half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward D, covering one-fourth the distance between where you are and D. Finally move toward E, covering one-fifth the distance between you and E, stop and dig.

(a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E, as shown in the figure. What are the coordinates of the point where his treasure is buried?

(b) Now rearrange the order of the trees [e.g., B (30 m, -20 m), A (60 m, 80 m), E (-10 m, -10 m), C (40 m, -30 m) and D (-70 m, 60 m)], and repeat the calculations to show that the answer does not depend on the order in which the trees are labeled.

Q4. An automobile tire is rated to last for 50 000 miles. To an order of magnitude, through how many revolutions will it turn? In your solution, state the quantities you measure or estimate and the values you take for them.

Last edited by a moderator: May 8, 2015
2. Sep 23, 2004

### christinono

in the first question, what do x, a and t stand for?

3. Sep 23, 2004

### Faiza

a denotes the acceleration
t denotes the time
x is the position or distance? :(

4. Sep 23, 2004

### Faiza

5. Sep 23, 2004

### christinono

I don't have much time, but I'll try and help U with the first one. The equation works if m and n are exponents. Are they?

6. Sep 23, 2004

### Tom McCurdy

I will provide help more than i should but this is the last time u will recieve this kind of help and the mentors may feel i am to generous and remove my posts and they may be wrong becasue I am going very quickly
Q2. a 6 *10 ^ 9/1000
then convert into days
b. (6 *10 ^ 9 * 15.5/10000)/6 378

7. Sep 23, 2004

### Tom McCurdy

Q3.
A (30 m, -20 m),
B (6 m, 8 m),
C (-10 m, -10m),
D (40 m, -30m),
E (-70 m, 60m),

(30+6)/2 (-20+8)/2 this will give you half way between A and B then
use this as your new cordinates and use the same method to get all your new points

8. Sep 23, 2004

### Tom McCurdy

Q4. C=pie*d
find a estimation for d being diameter
then find out the circumference of a tire
then take mile/circumfernce (in miles)
then multiply by 50,000

9. Sep 25, 2004

### Faiza

Thanks christinono & Tom McCurdy, I appreciate it! You've given me much to think about. I was able to solve the problems :)

10. Sep 25, 2004

### Faiza

I need some remedial help lol!

*FREE FALLING OBJECTS*

Q. A boy stands at the edge of a bridge 20.0 m above a river
and throws a stone straight down with a speed of 12.0 m/s.
He throws another pebble straight upward with the same
speed so that it misses the edge of the bridge on the way
back down and falls into the river. For each stone find (a)
the velocity as it reaches the water and (b) the average
velocity while it is in flight.

Note: Ignore the affects of air resistance.
I'm so lost, i read about free fall acceleration cant get this one!

11. Sep 25, 2004

### Hypercase

I can help with part a:
suppose the boy threw the first stone straight down with speed v.
now if the second stone is thrown verically upward at the same speed v(speed not velocity)from the bridge, on its domnward path when it passes the bridge it will have the same speed it was thrown up with ie, v. Now the second stone has speed v and direction towards the water, this is similar to motion of stone 1.
Thus they both hit the water at the same speed.

12. Sep 25, 2004

### decibel

For 2a i got approx. 190 years, but i did this very quickly so i might be wrong.

13. Sep 25, 2004

### JasonRox

I can't believe people wait until the last minute.
I do it sometimes, but I sure don't rely on some guy online to help me out.

14. Sep 26, 2004

### Faiza

I dont usually procrastinate, a friend recommeded this forum and i thought maybe someone could help me out