Why does the displacement force act on AC - BC?

[nb2000]

Homework Statement

If the 75-kg crate starts from rest at A, determine its speed
when it reaches point B. The cable is subjected to a constant
force of F = 300N. Neglect friction and the size of the
pulley.

Relevant Equations

The principal of Work and Energy

Hi,

I am having trouble understanding the intuition behind the problem I attached.

Work is the product of the force and displacement in the direction of displacement, so since the crate is moving horizontally from A to B why isn't the displacement AB = 6m?

Thanks in advance

 

[kuruman]

The displacement of the crate is indeed 6 m. As you say "Work is the product of the force and displacement in the direction of displacement". If you want to consider the force at the point where the rope it is attached to the crate, the angle between the force and the horizontal displacement changes continuously and is never along the displacement. This makes the calculation more involved. Try doing it that way and you will see what I mean. It is much easier to consider the "force in the direction of the displacement" on the other side of the pulley where the force is always along the displacement. Since you know the force all you have to do is calculate the new displacement which, of course, is not 6 m.

 

[haruspex]

Work is the product of the force and displacement in the direction of displacement

That is not quite right, and may be misleading you.
Work is the product of the displacement and (force in the direction of displacement).
Or, equivalently,
Work is the product of the force and (displacement in the direction of the force).