The final one! ...AB is a rigid rod in an upright position and at its end B is a flexible rope....

[Student_needs_help]

I need the answer and equation if someone can help, because i am lost on this one.

In the accompanying figure, AB is a rigid rod in an upright position and at its end B is a flexible rope that rotates through point-like rollers at C and D to E, where a weight is attached to the rope. How much does the weight at step E rise when the rod AB is pivoted into the pan?

 

[HallsofIvy]

What "pan" is intended here? There is no mention of a "pan" until the final question! I suspect what is mean is that the originally vertical AB becomes horizontal. Okay what is the distance from B in the rods vertical position to B in the rod's horizontal position (Pythagorean theorem)? That is the distance the weight will rise.

 

[Student_needs_help]

What "pan" is intended here? There is no mention of a "pan" until the final question! I suspect what is mean is that the originally vertical AB becomes horizontal. Okay what is the distance from B in the rods vertical position to B in the rod's horizontal position (Pythagorean theorem)? That is the distance the weight will rise.

My bad, it was a mistake. This is the right one.

In the accompanying figure, AB is a rigid rod in an upright position and at its end B is a flexible rope that rotates through point-like rollers at C and D to E, where a weight is attached to the rope. How much does the weight at step E rise when the rod AB is turned horizontally?

 

[MarkFL]

Initially, the amount of rope that is over the roller at C is 0.5 m. We'll call this initial amount (in meters):

[MATH]C_i=0.5=\frac{1}{2}[/MATH]
Then the final amount will be the hypotenuse of a right triangle having legs 2.0 and 2.5 meters in length:

[MATH]C_f=\sqrt{2.0^2+2.5^2}=\frac{\sqrt{41}}{2}[/MATH]
And so the distance the weight at E will rise is the difference between the two. Can you state this difference?