Question

(A) At rest, a spaceship has length Lo. In motion at speed v, its length is measured by external observers (at rest) to be L. What is the speed v in terms of the speed of light?

(B) In the kitchen of the spaceship the chef sets the oven timer for 2 hours to bake a cake. How much time will the cake spend in the oven, as measured by the external observers?
(A)--------------
(b)------------

Answer 1

Final answer:

In special relativity, the length contraction formula is used to calculate the measured length of a spaceship in motion. The formula for time dilation is used to calculate the measured time in the oven for external observers.

Step-by-step explanation:

(A) The length contraction phenomenon in special relativity states that the length of an object appears shorter when it is moving relative to an observer. The formula to calculate the contracted length is given by:

L = L0sqrt(1 - (v2/c2))

Where L is the length measured by the observer, L0 is the rest length of the spaceship, v is the speed of the spaceship, and c is the speed of light in a vacuum. Rearranging the formula, we can solve for v:

v = c×sqrt(1 - (L2/L02))

(B) According to time dilation in special relativity, time appears to run slower for an object in motion relative to an observer. The formula to calculate the dilated time is given by:

t = t0 / sqrt(1 - (v2/c2))

Where t is the measured time by the observer, t0 is the proper time (time on the spaceship), v is the speed of the spaceship, and c is the speed of light in a vacuum. In this case, the proper time set by the chef is 2 hours, so we need to solve for t:

t = t0 / sqrt(1 - (v2/c2)) = 2 / sqrt(1 - (L2/L02))

Learn more: