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titansarus
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Homework Statement
Question from Fundamentals of Physics (Halliday, Resnick, Walker)
This figure below shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height ##h = 1.20 m##, so the cart slides from ##x1 = 3.00## m to ##x2 = 1.00 m##. During the move, the tension in the cord is a constant ##25.0 N##.What is the change in the kinetic energy of the cart during
Homework Equations
##\int dw = \int F . dr##
The Attempt at a Solution
At first we get that ##x/1.2 = cot \theta## so ##dx = -1.2 (1 + cot ^ 2 \theta) d\theta ##
Now I don't know whether to integrate the FIRST Or SECOND: (angles from ##x_1=3## to ##x_2=1## change from##\theta_1 = 0.380506377## to ##\theta_2 = 0.87605805059## radian)
FIRST: ##W= \int dw = \int _3^1 25 . dx = \int _{0.380}^{0.876} 25 * 1.2 (1 + cot ^ 2 \theta) d\theta = 41.67 J##
or using $$F = 25 cos \theta$$ and
SECOND: ##W= \int dw = \int _3^1 25 cos\theta . dx = \int _{0.380}^{0.876} 25 * cos \theta * 1.2 (1 + cot ^ 2 \theta) d\theta = 34.77 J##
The book itself solved it with another solution using pythagoras theorem and got the first answer but I want to solve it using angles and don't know why the first one gives the answer of the book. I think second one makes more sense.