An object moving in the xy plane experiences two forces given by the following f
ID: 2258771 • Letter: A
Question
An object moving in the xy plane experiences two forces given by the following functions:1 = (-4x2 N/m2) + (-7y N/m)
2 = 3 N, always in the direction of motion
Calculate the total work done by each force when an object is moved from the origin to (x,y)=(+3 m,+ 4 m):
a.) in a straight line.
W1 = J
W2 = J
b.) first moved parallel to the +x and then parallel to the +y axis.
W1 = J
W2 = J
c.) Calculate the total work done by each force moving from the origin to (x,y)=(+3 m, +4 m) and back (moving both there and back in a straight line).
W1 = J
W2 = J An object moving in the xy plane experiences two forces given by the following functions:
1 = (-4x2 N/m2) + (-7y N/m)
2 = 3 N, always in the direction of motion
Calculate the total work done by each force when an object is moved from the origin to (x,y)=(+3 m,+ 4 m):
a.) in a straight line.
W1 = J
W2 = J
b.) first moved parallel to the +x and then parallel to the +y axis.
W1 = J
W2 = J
c.) Calculate the total work done by each force moving from the origin to (x,y)=(+3 m, +4 m) and back (moving both there and back in a straight line).
W1 = J
W2 = J An object moving in the xy plane experiences two forces given by the following functions:
1 = (-4x2 N/m2) + (-7y N/m)
2 = 3 N, always in the direction of motion
Calculate the total work done by each force when an object is moved from the origin to (x,y)=(+3 m,+ 4 m):
a.) in a straight line.
W1 = J
W2 = J
b.) first moved parallel to the +x and then parallel to the +y axis.
W1 = J
W2 = J
c.) Calculate the total work done by each force moving from the origin to (x,y)=(+3 m, +4 m) and back (moving both there and back in a straight line).
W1 = J
W2 = J
Explanation / Answer
a) work doneby F1, W1 = integral F1x*dx + integral F1y*dy
= integral -4*x^2*dx + integral -7*y*dy
= -4*x^3/3 - 7*y^2/2 (here x is changeing from 0 to 3 and y is changing from 0 to 4)
= -4*3^3/3 - 7*4^2/2
= -92 J
work done by F2, W2 = F2*d = 3*sqrt(3^2+4^2) = +15 J
b)
work doneby F1, W1 = integral F1x*dx + integral F1y*dy
= integral -4*x^2*dx + integral -7*y*dy
= -4*x^3/3 - 7*y^2/2 (here x is changeing from 0 to 3 and y is changing from 0 to 4)
= -4*3^3/3 - 7*4^2/2
= -92 J
work done by F2, W2 = F2*x + F2*y = 3*3 + 3*4 = 21 J
c)
W1 = 0
w2 = F2*d + F2*d = 2*F2*d = 2*3*sqrt(3^2+4^2) = 30 J