The Ladder is 5 m long and weighs 180N. The guy weighs 800N, and stops 1m horizontally up the ladder. The bottom of the ladder rest on a horizontal stone ledge at 53.1 degree.
Find the normal and he frictional force at the base.
HELP!!!
draw the figure.
lable the forces. At the top of the ladder, you have a horizontal force only pushing intothe wall, and the wall pushing back.
You have on the ladder at center, weight, and the guy 1 m upwards,
You have the base of the ladder, vertical, and friction force.
Now write equilibirum equations.
Sume horizontal forces=0
sum vertical forces =0
sum moment about any point (I recommend the base of the ladder)=0
You will get a solution quickly.
To find the normal and frictional force at the base of the ladder, we need to analyze the forces acting on the ladder and the guy.
First, let's identify the forces acting on the ladder:
1. Weight of the ladder (180N) acts downward from its center of mass.
2. Normal force from the stone ledge acts perpendicular to the ledge.
3. Frictional force from the stone ledge acts parallel to the ledge.
Now, let's take a look at the forces acting on the guy:
1. Weight of the guy (800N) acts downward from his center of mass.
To proceed, we need to resolve the forces into vertical and horizontal components. Let's consider the vertical components first:
The vertical forces acting on the ladder are:
1. Weight of the ladder (180N) pointing downward.
2. Normal force from the stone ledge pointing upward.
Since the ladder is at rest in the vertical direction, the sum of these forces must be zero. Therefore, the normal force is equal to the weight of the ladder (180N).
Next, let's consider the horizontal components:
The horizontal forces acting on the ladder are:
1. Frictional force from the stone ledge acting in the direction opposite to the ladder's motion.
2. Horizontal component of the normal force acting in the same direction as the ladder's motion.
Since the guy stops 1m horizontally up the ladder, there is no horizontal acceleration. As a result, the sum of the horizontal forces must also be zero. Therefore, the horizontal component of the normal force is equal to the frictional force.
To calculate the frictional force, we need to find the horizontal component of the normal force using trigonometry:
Horizontal component of normal force = Normal force * cos(53.1°)
Now we can calculate the values:
1. Normal force = Weight of the ladder = 180N
2. Frictional force = Horizontal component of normal force = Normal force * cos(53.1°)
By substituting the value of the normal force into the equation for the frictional force, we can find the values of the normal and frictional forces at the base of the ladder.