Physics 161 Summer 2003 Homework 1

E. Gortcheva Due June 5, start of class

 

 

Read Serway & Beichner (S&B): app. B and chaps. 1, 3, 7.2, 11.2, and 2.

 

1.      S&B 1.3

2.      If ``jerk'' is defined as

\begin{displaymath}j = \frac{{\rm d}^3 x}{{\rm d}t^3} \, ,
\end{displaymath}


where x has dimensions of [L] and t has dimensions of [T], what are the dimensions of j?

3. In the equation

\begin{displaymath}\phi = \tan^{-1} \left(\frac{Rg \cos(\theta)}{v^2}\right) \, ,
\end{displaymath}


g has dimensions of [L/T2] and R has dimensions of [L].

(a) What are the dimensions of $\theta$?

(b) What are the dimensions of v?

(c)What are the dimensions of $\phi$?

 

4. You are given the equation

\begin{displaymath}mg - b v_t = 0 \, ,
\end{displaymath}


where m has dimensions of [M], g has dimensions of [L/T2], and vt has dimensions of [L/T]. What are the dimensions of b?

 

5. S&B 1.20

6. S&B 1.28

7. S&B 1.40

 

8. Carol has a mass of 65 kg. Assume that a typical cell is a sphere with a diameter of 10 $\mu$m and a density of 1 g/cm3, and that 80% of Carol's mass is in her cells. Make an order-of-magnitude estimate of the number of cells in Carol's body.

 

9. S&B 1.48

 

10. S&B 1.52