A force , where is a positive constant, acts on a particle moving in the plane. Starting from the origin, the particle is taken along the positive -axis to the point , and then parallel to the -axis

Question

A force , where  is a positive constant, acts on a particle moving in the  plane. Starting from the origin, the particle is taken along the positive -axis to the point , and then parallel to the -axis to the point . The total work done by the force on the particle is

Canvas Classes · Accepted Answer

🧠 Position-Dependent Force on a Two-Leg Path → Do Each Leg Separately

The force  changes with position, and the particle moves along two straight legs. On each leg one coordinate is held fixed, so only part of the force does work. The smart first move is to split the journey: first  along the -axis, then  parallel to the -axis.

🗺️ Working It Out

Leg 1 — along the -axis, so  and :
 (because  the whole way). Work .

Leg 2 — parallel to the -axis, so  is fixed and :
.
.

Total work .

⚡ The Sm

More questions from this chapter

More questions from this chapter