Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
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After picking up passengers, a train accelerates uniformly until its speed is 100 km/hr at t= 300 s. If during this time it is traveling on a planar path that approximates the circle and line shown in the figure, find the magnitude of the train's acceleration when (a) t = 1 min and (b) t = 2 min.
link to figure:
http://i22.photobucket.com/albums/b346/ … 2-0017.jpg
I'm not sure what frame of reference to use, n-t frame or r-t frame or a combination of both, and how to start this problem, ANY help will be GREATLY APPRECIATED, I have been trying to figure this out for hours, including last night, I just don't know how to piece it all together, I think there should be a delta theta, because in the figure the radius is changing after that point where it says start, at least thats what I am thinking, still completely lost, PLEASE HELP!!!
normal acceleration is v^2/r
tangental acceleration is dv/dt
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The train's trajectory during the acceleration consists of two parts. The first part is a circular arc l=r*π/3 = 523 m long. The second part is a line segment. The tangential acceleration is a(tang) = Δv/Δt = 100/(3.6*300) = 0.0923 m/s^2.
The distance covered after 1 m = 60 secs x(60) = a(tang)*t^2/2 = 0.0923 m/s^2 = 166 m
We see that x(60)<l. It means train's still on the circle and it has also normal acceleration a(norm) = (v(t))^2/r, where v(t) = a(tang)*t .
Thus a(norm)(60) = 0.0111 m/s^2;
and a(60) = sqrt((a(tang))^2+(a(norm))^2) = 0.0930 m/s^2;
When t=120s x = 665>523m therefore train's on the line segment and a(norm) = 0 and a = a(tang) = 0.0923 m/s^2.
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