A 14.5 m uniform ladder weighing 480 N rests against a frictionless wall. The la

Question

A 14.5 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 57.0 ° angle with the horizontal.

(a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 830 N firefighter is 4.00 m from the bottom.

Magnitude of the horizontal force

I keep getting 320.67 N, and it's within 10% of the value, which is incorrect.

_____ N Direction -----> Towards the Wall or Away from the Wall?

Magnitude of the vertical force

______ N Direction -----> Up or Down?

(b) If the ladder is just on the verge of slipping when the firefighter is 9.40 m up, what is the coefficient of static friction between ladder and ground?

Explanation / Answer

It is not clear what 4m from bottom means. Is it along the ladder or is it the vertical distance. I am assuming it is along the ladder.

1. Do horizontal force equilibrium: RX1=RX2 where RX1 is the horizontal reaction from the base ground and RX2 = horizontal reaction from the vertical wall.

2. Take moment about base:

480 x 7.25cos(57) + 830 x 4cos(57) = RX2 x 14.5sin(57)

==> RX2 = 304.54N

This is the value of RX1 as well

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.