Question

An object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m

Answer 1

The work done by the applied force on the object is (2ab²i + 3b²j) J.

Magnitude of the force on the object

The magnitude of the force on the object is calculated as follows;

f = (2xyi + 3yj)

when;

x = a, and y = b

f = (2abi + 3bj)

Work done by the force

The work done the applied force is the product of force and displacement of the object.

W = fΔs

where;

• Δs is displacement of the object

Δx = a - a = 0

Δy = 0 - b = -b

Δs = √(Δx² + Δy²)

Δs = √(-b)²

Δs = b

W = (2abi + 3bj) x b

W = (2ab²i + 3b²j) J

Thus, the work done by the applied force on the object is (2ab²i + 3b²j) J.

The complete question is below;

An object moving in the xy-plane is subjected to the force f = (2xyi + 3yj),  where x and y are in m. 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: brainly.com/question/8119756