Apparent forces problem, train of average speed and a difference in weight

[Trish1234]

Homework Statement

While taking an eastbound train to work, a passenger of fixed mass finds that she weighs 542N. On the way home she weighs herself again while the train is at full speed and finds she weighs 543N. If she works 50km from home, how long is her commute if she lives at 40°S? (You may assume the average speed of the train is its full speed.)

Homework Equations

Dv/Dt=-fu
f=2Ωsinθ
Ω=7.292x10^-5 s^-1
F=-2Ω(sinθ)Mu

The Attempt at a Solution

First I tried solving the first equation for Dv/Dt getting -0.004687 km/s and didn't know where to go from here to find the time. Although I didn't feel right about it because I never used M. Then I found the last equation which includes M but I still don't know how to derive time from that equation. I know the solution is 10min, 18s but I don't know how to get that answer. Thank you for any help!

 

[anathema]

Thank you for your post. I am a scientist and I will be happy to help you with this problem.

First, let's review the given information. The passenger weighs 542N while the train is traveling eastbound at full speed, and 543N while the train is traveling back home at full speed. We also know that the passenger works 50km from home and lives at 40°S.

To solve for the time of the commute, we need to use the equations you have provided. The first equation, Dv/Dt=-fu, relates the change in velocity (Dv) to the force (f) and mass (M) of the passenger. However, we do not have enough information to use this equation to solve for time.

The second equation, f=2Ωsinθ, relates the force (f) to the Coriolis parameter (Ω) and the latitude (θ) of the passenger. We can use this equation to calculate the force acting on the passenger during the commute.

The third equation, F=-2Ω(sinθ)Mu, relates the force (F) to the Coriolis parameter (Ω), the sine of the latitude (sinθ), the mass of the passenger (M), and the change in velocity (u). This equation can be rearranged to solve for the change in velocity (u).

Now, let's plug in the given information into these equations. We know that the Coriolis parameter, Ω, is 7.292x10^-5 s^-1. We also know that the latitude of the passenger, θ, is 40°S, which is equivalent to -40° in the equation. We can calculate the force acting on the passenger using the second equation:

f=2Ωsinθ
=2(7.292x10^-5 s^-1)(sin(-40°))
= -0.000097 N

Next, we can use the third equation to solve for the change in velocity (u):

F=-2Ω(sinθ)Mu
u = F/-2Ω(sinθ)M
= -0.000097 N/-2(7.292x10^-5 s^-1)(sin(-40°))(fixed mass)
= 0.004687 km/s

Now, to find the time of the commute, we can use the formula d=vt, where