- #1
kitsh
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Homework Statement
A truck hauling a big tank of oil starts at position x=D (Chicago) and heads due west (–x direction) toward its destination at x = 0 (Des Moines). At Chicago, the total mass of the loaded truck is M and the mass of oil it is carrying is λM. (Thus M(1–λ) is the "tare" mass = the mass of the truck when it is empty.) The driver starts from rest at time t = 0 with his engines set to deliver a constant force of magnitude F throughout the trip.
Unfortunately, the trucker's oil tank is leaking: it is losing oil at a constant rate-per-unit-distance of dm/dx=λM/D
Ignore the small change in m from the truck's consumption of gasoline (it's tiny compared to the truck's mass).
(a) Calculate m(x) in terms of x and the given constants D, M, λ, and/or F.
(b) Calculate the truck's kinetic energy as a function of x and the given constants.
(c) At what position x does the truck reach it's maximum speed and at what position does it reach it's maximum kinetic energy?
Homework Equations
dm/dx=λM/D
F=dp/dt
T=.5mv²
The Attempt at a Solution
I think I've got part a right as λ, M, and D are constants so:
m(x)=λMx/D+(1-λ)M
and I checked it where x=D the mass is M, so I think that is the right answer.
As for parts b and c , I honestly have no idea where to begin solving for velocity. I understand to find T that I'll have to use my m(x) but I don't know what force equation to set up to solve for velocity.