Answer:
The frictional force must be 28.3 N ( option C)
Step-by-step explanation:
Step 1: Data given
Length of the ladder = 3.00 meter
The ladder eighs 200 N
Distance away from the wall = 1.00 meter
Center of mass of the ladder is 1.20 m from its base
Step 2: Calculate the height of the ladder
Let's consider the space between the ladder and the wall as a right triangle.
Pythagoras says:
Base² + Height² = Hypotenuse²
with base = 1.00 meter
with height = TO BE DETERMINED
with hypotenuse = 3.00 meter
1²+ h² = 3²
1 + h² = 9
h = √8
Step 3: Calcuate the angle between ladder and floor
Consider the angle θ = the angle the ladder makes with the floor
Sin θ = h/L = √8/3
sin θ = 0.9428
cos θ = 1/3
θ ≈ 70.5°
Step 4: Calculate torque
Since the center of mass is 1.20 m from the ladder’s base,
the torque, caused by the ladder’s weight, can be calculated as followed:
dh = 1.2 * cosθ = 1.2 * 1/3 = 0.4m
Torque = 200N * 0.4m = 80
This is the counter clockwise torque.
Step 5: Calculate frictional force
The force from the wall on the top of the ladder, is one of the horizontal forces. The friction force is the other horizontal force. These two forces are equal.
The vertical distance from the wall force to the floor is equal to the height of the right triangle.
Torque = F * h
F = torque /h
F = 80 ÷ √8
F = 28.28 ≈ 28.3 N
The frictional force must be 28.3 N ( option C)