Observer A measures the length of two rods, onestationary, the other moving with

Question

Observer A measures the length of two rods, onestationary, the other moving with a speed of 0.945c. She finds that the rods have the samelength, L0. A second observer Btravels along with the moving rod. (a) What is the length observerB measures for the rod in observer A's frame? (Express your answer to three decimal places.)
Enter amathematical expression. 1


(b) What is the ratio of the length of A's rod to thelength of B's rod according to observerB?
Enter anumber. 2 Enter amathematical expression. Enter anumber.

Explanation / Answer

.    L = L0 / .
where L0 denotes the proper length, and = 1 / sqrt ( 1-(v/c)2 )
.
First, I'll assume A's rod is the stationary rod in A's frame, andB's rod is the stationary rod in B's frame. . Hence     L = L0 * sqrt( 1- (0.945 c/c)2 ) = 0.3270   L0 . (b) In B's inertial reference frame, the equationfor A's rod is L=(Lo)/, . and the equation for B's rod is (Lo) =L1/ ==> L1=(Lo). .
The ratio of A's rod to B's rod according to B is then : .
A / B   = [ ((Lo) / ) / (Lo * ) ] = 1/²  

In this case, = 1 / sqrt ( 1- (0.945 c/c)2 )  ˜ 3.0. . So A's rod is approx. 9 times smaller than B's rod accordingto B. . Hope this helps u!

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.