Question

14.0 m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a 65.0°-angle with the horizontal. (a) Find the horizontal and vertical forces (in N) the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.10 m along the ladder from the bottom. horizontal

Answer 1

The horizontal reaction force is 230.3 N.

Step-by-step explanation:

Given that,

Length l= 14.0 m

Weight of ladder F = 490 N

Angle = 65°

Weight of firefighter F'= 850 N

Height l'= 4.10 m

Suppose horizontal force magnitude N direction vertical force magnitude N direction

We need to calculate the horizontal reaction force

Horizontal reaction force = normal reaction from wall

Vertical reaction force = weight of ladder +weight of man

`F=490+850`

`F=1340\ N`

We need to calculate the moment about bottom is zero

`N* l\sin\theta=F*(l)/(2)\cos\theta+F'* l'\cos\theta`

Put the value in the equation

`N*14\sin(65)=490*7\cos(65)+850*4.10\cos(65)`

`N=(490*7\cot(65)+850*4.10\cot(65))/(14)`

`N=230.3\ N`

Hence, The horizontal reaction force is 230.3 N.