Determine work in circular motion

[Calpalned]

Homework Statement

An object, moving along the circumference of a circle with radius $R$, is acted upon by a force of constant magnitude F. The force is directed at all times at a $30 \degrees$ angle with respect to the tangent to the circle. Determine the work done by this force when the object moves along the half circle from A to B.

Homework Equations

N/a

The Attempt at a Solution

My solutions guide tells me to us $\int (Fcos \theta dl)$ The question stated "constant force", so why do we need to integrate? Why can't I use F dot D?

Thank you!

By the way, how do I write in limits for integration?

 

[SammyS]

Homework Statement

An object, moving along the circumference of a circle with radius $R$, is acted upon by a force of constant magnitude F. The force is directed at all times at a $30 \degrees$ angle with respect to the tangent to the circle. Determine the work done by this force when the object moves along the half circle from A to B.

Homework Equations

N/a

The Attempt at a Solution

My solutions guide tells me to us $\int (Fcos \theta dl)$ The question stated "constant force", so why do we need to integrate? Why can't I use F dot D?

Thank you!

By the way, how do I write in limits for integration?

limits for integration: _lower ^upper , i.e. subscript, superscript . Degrees: ^\circ

F is not constant. Its magnitude is constant.

What do you mean by D ? "Why can't I use F dot D"

 

[haruspex]

If by D you mean the distance element vector $\vec {dl}$ then $F \cos(\theta)dl = \vec F . \vec D$.