Homework Help: Pre Calc

Posted by Em on Wednesday, May 25, 2011 at 7:06pm.

Find the work done by a force F of 30 pounds acting in the direction (2,3) in moving an object 3 feet from (0,0) to the point in the first quadrant along the line y = (1/2)x.
The answer is 85.38 foot-pounds.
I just need to figure out how to get the answer.

Pre Calc - Damon, Wednesday, May 25, 2011 at 7:32pm
Find the angle of the Force F
cos T = 2/sqrt13 = .555
T = 56.3 deg above x axis
or
tan T = 2/3
so T = 56.3

Find the direction of motion from slope of line
tan slope = 1/2
slope angle = 26.6 deg

angle between force and motion = 56.3-26.6 = 29.7 degrees
so
component of force in direction of motion = 30 cos 29.7
= 26.06 pounds
26.06*3 = 78.2 ft lbs
beats me how to get 85.38

It would be much closer if the force vector were direction(3,2)
Pre Calc - Megha, Wednesday, January 30, 2013 at 9:11pm
the vector is actually <2,2>
and the line angle is 64.3

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