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

Answer:

The horizontal reaction force is 230.3 N.

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

$N\times l\sin\theta=F\times\dfrac{l}{2}\cos\theta+F'\times l'\cos\theta$

Put the value in the equation

$N\times14\sin(65)=490\times7\cos(65)+850\times4.10\cos(65)$

$N=\dfrac{490\times7\cot(65)+850\times4.10\cot(65)}{14}$

$N=230.3\ N$

Hence, The horizontal reaction force is 230.3 N.