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Homework Statement
Figure 740 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 = 1.6 m, so the cart slides from x1 = 4.0 m to x2 = 1.0 m. During the move, the tension in the cord is a constant 27.0 N. What is the change in the kinetic energy of the cart during the move?
Picture Attached
Answer: 65.376061721000Units J
Homework Equations
Work energy thorem Delta K=W= Fd cos (theta)
The Attempt at a Solution
The first thing I tried with a friend was simply fdcos (theta) but then we realized that the angle is constantly changing. So we integrated Fd cos(theta) d(theta) from theta(at x1) to theta(at x2) but we got the wrong answer. We were stumped and so we asked another friend who reminded us that when you integrate d(theta) that you are integrating over an arc length rather than a linear distance. So we figured that you can turn the distance into a function of theta and it is no longer a constant. Or integrate over distance and make theta a function of distance. This seems like it would work but it gives a really gnarly integral with a cos and a tangent. That brings up red flags that it should be easier than that for an intro course at a JC where we only sometimes do basic integrals.
Thanks
Homework Statement
Homework Equations
The Attempt at a Solution
Homework Statement
Homework Equations
The Attempt at a Solution
Homework Statement
Homework Equations
The Attempt at a Solution
Homework Statement
Homework Equations
The Attempt at a Solution
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