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Sagot :
The magnitude of the work done by force experience by the object is (2a²b + 3b²)J.
Work done by the force experienced by the object
The magnitude of the work done by force experience by the object is calculated as follows;
W = f.d
where;
- F is the applied force (2xyi + 3yj), where x and y are in meters
- d is the displacement of the object = (a, b)
The work done by the force is determined from the dot product of the force and the displacement of the object.
F = (2xyi + 3yj).(a + b)
W = (2abi + 3bj).(ai + bj)
W = (2a²b + 3b²)J
Thus, the magnitude of the work done by force experience by the object is (2a²b + 3b²)J.
The complete question is below:
The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis.
How much work does the force do?
Learn more about work done here: https://brainly.com/question/8119756
The total work done for an object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m is 3ab N.
What is work done?
Work done is the force applied on a body to move it over a distance. Work done for inclined plane can be given as,
[tex]W=F\times d[/tex]
Here (F) is the magnitude of force and (d) is the distance traveled.
An object moving in the xy-plane is subjected to the force
[tex]\vec f =(2xy\hat i +3y\hat j)[/tex]
Here, x and y are in meter.
The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis.
- (a) How much work does the force do?
For the first part, the particle moves along x-axis. It moves zero along x-axis. Thus, the force, as y=0.
[tex]W_1=\int\limits^a_0 {2xy\hat i} \, dx =0\\[/tex]
Now, when the object moves along y-axis,
[tex]W_2=\int\limits^a_0 {3y\hat j} \, dx \\W_2=3\int\limits^b_0 {y\hat j} \, dx\\W_2=3y(a-0)\\W_2=3ba\\W_2=3ab[/tex]
Total work done,
[tex]W=0+3ab\\W=3ab\rm\; N[/tex]
Thus, the total work done for an object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m is 3ab N.
Learn more about the work done here;
https://brainly.com/question/25573309
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