A uniform 250 N ladder rests against a perfectly smooth wall, making a 35 degree angle with the wall. (a)Draw a free body diagram of the ladder. (b) Find the normal forces that the wall and the floor exert on the ladder. (c) What is the friction force on the ladder at the floor?
I have the free body diagram, just not sure how to continue..any help is appreciated
write the following equations.
sum of vertical forces=0
sum of horizontal forces=0
sum of moments about any point =0
I recommend using the base of the ladder as the moment sum point.
Those three equations will do it. Don't forget the weight of the ladder at the MIDDLE of the ladder.
To continue solving this problem, let's analyze the forces acting on the ladder.
(a) Free Body Diagram:
Draw a diagram representing the ladder as a straight line, representing its length, leaning against the wall. At the bottom of the ladder, draw a vertical line to represent the ground. Attach the following forces to the ladder:
- A force of weight (W) acting straight downward from the center of mass of the ladder (in this case, 250 N).
- A normal force (N₁) perpendicular to the wall at the point of contact between the wall and the ladder.
- A frictional force (f) acting parallel to the floor.
(b) Normal Forces:
Since the ladder is at rest, the sum of the vertical forces must be zero. Therefore, the normal force (N₂) exerted by the floor on the ladder must balance the vertical component of the weight of the ladder.
Using trigonometry, we can determine that N₂ = W * cos(35°).
Since the ladder is in equilibrium horizontally, the sum of the horizontal forces must also be zero. Therefore, the normal force (N₁) exerted by the wall on the ladder and the frictional force (f) must balance the horizontal component of the weight of the ladder.
We can determine that N₁ = W * sin(35°) and f = N₁.
(c) Friction Force:
The frictional force (f) on the ladder at the floor is equal to N₁, which we previously found to be equal to W * sin(35°).
Now you can substitute the given values into the equations to find the values for N₂, N₁, and f.