Answer to Question #306961 in Mechanics | Relativity for Ria

Question

4. A uniform 15 kg ladder 3 m long rests against a frictionless wall at a point

2.4 m off the floor. Find the horizontal and vertical components of the force exerted by the ladder on the floor.

Answer 1

Explanations & Calculations

• Since there is no friction from the wall, there is only the reaction force that acts on the ladder at the wall and it is horizontal in the overall picture. Say that is R.
• At the bottom, however, is needed some friction to hold the ladder hence there exist both vertical and horizontal components, say S and f respectively.
• Upon consideration of the equilibrium horizontally, it is obvious that f = R and similarly from the vertical equilibrium S = mg.
• Therefore,

$\qquad\qquad \begin{aligned} \small S&=\small 15\,kg\times9.8\,ms^{-2}\\ &=\small 147.0\,N \end{aligned}$

• To find out f (or R what may seem easy), take moment around the bottom point of the ladder.

$\qquad\qquad \begin{aligned} \small R\times2.4-mg\times1.5\cos\theta&=\small 0\\ \small R&=\small \frac{1}{2.4}\Big(147.0\,N\times1.5\times\frac{3}{5}\Big)\\ &=\small 55.1\,N\\ &=\small f \end{aligned}$