MoodersMaths
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- Joined
- Jun 1, 2017
- Messages
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Having some problems with this question :
Show that the work done by the force F=(3xy+4)i + y^3j moving anti clockwise around the boundaries of the triangle defined by the points (0,0),(3,0) and (3,3) is -27
from what i figured out you figure out the value of y or x as a function of one another for each line and use the other as a boundary
so for the first line (0,0) to (3,0) i had x from 0 to 3 and y=0
so i equated y to 0 in the force equation which left with the 4 i integrated 4 from the limits 0 to 3 which was 12
I did the same thing for the next part where x=3 and y is from 0 to 3 because x didnt change i assumed dx would be 0 removing the first part of the equation leaving me with just y^3 to integrate with limits 0 to 3 which gave me 20.25.
I calculated the last line from 3,3 to 0,0 I found y=x as they both go from (3,3) to (0,0) so i substituted x in the place of both y's in the question and then used y = x to get dy = x^2 dx so i multiplied the x^3 that was previously y^3 by x^2 i then integrated the equation however after integrating i got -160.5 as my answer 3x^3 /3 + 4*3 + 3^6/6. i integrated these from 3 to 0 so they were all negatives. I can't figure out how to get -27 as all of my answers seem to be way past that.
Show that the work done by the force F=(3xy+4)i + y^3j moving anti clockwise around the boundaries of the triangle defined by the points (0,0),(3,0) and (3,3) is -27
from what i figured out you figure out the value of y or x as a function of one another for each line and use the other as a boundary
so for the first line (0,0) to (3,0) i had x from 0 to 3 and y=0
so i equated y to 0 in the force equation which left with the 4 i integrated 4 from the limits 0 to 3 which was 12
I did the same thing for the next part where x=3 and y is from 0 to 3 because x didnt change i assumed dx would be 0 removing the first part of the equation leaving me with just y^3 to integrate with limits 0 to 3 which gave me 20.25.
I calculated the last line from 3,3 to 0,0 I found y=x as they both go from (3,3) to (0,0) so i substituted x in the place of both y's in the question and then used y = x to get dy = x^2 dx so i multiplied the x^3 that was previously y^3 by x^2 i then integrated the equation however after integrating i got -160.5 as my answer 3x^3 /3 + 4*3 + 3^6/6. i integrated these from 3 to 0 so they were all negatives. I can't figure out how to get -27 as all of my answers seem to be way past that.
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