Draw the figure. You have the following equations that you can write:
a) Sum Vertical Forces=0
b) Sum horizontal forces=0. Remember that at the upper part of the ladder, there is a horizontal force (only).
c) Sum of moments about any point, I suggest the base of the ladder as that point. Remember that on moments it is the force x the distance to the Perpendicular to the force.
These equations will allow you to solve.
I will be happy to check your equations.
I just need help finishing this one off...again any help would be greatly appreciated:o)
An 85 kg person stands on a uniform ladder that is 4.3 m long and weighs 57.5 N. The floor is rough; hence it exerts both a normal force, f1, and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3. Use the dimensions in the figure to find the following. (a = 3.8 m.)
(a) Find the forces exerted on the ladder when the person is halfway up the ladder.
f 1 =
To find the forces exerted on the ladder when the person is halfway up the ladder, we need to analyze the forces in equilibrium.
First, let's define the forces acting on the ladder:
- The weight of the ladder (57.5 N)
- The normal force from the floor (f1)
- The frictional force from the floor (f2)
- The normal force from the wall (f3)
To draw the figure, we can use the following steps:
1. Draw a vertical line to represent the ladder.
2. Mark the midpoint of the ladder (halfway up) and label it as M.
3. Draw a horizontal line from point M to represent the force exerted by the wall (f3).
- Note that this line should not cross the ladder but should be tangent to it, as there is no friction between the wall and the ladder.
4. Draw a vertical line from the midpoint (M) to represent the normal force from the floor (f1).
5. Draw a horizontal line from the midpoint (M) to the right, representing the frictional force from the floor (f2).
6. Finally, label the weight of the ladder (57.5 N) acting vertically downwards.
Now that we have the figure, we can analyze the forces using the given equations:
a) Sum Vertical Forces = 0:
Since the ladder is in equilibrium, the sum of vertical forces must be equal to zero. This can be written as:
f1 + weight of the ladder = 0
b) Sum Horizontal Forces = 0:
Since the wall exerts only a normal force (f3) and there is friction between the ladder and the floor (f2), the sum of horizontal forces must be equal to zero. This can be written as:
f2 + f3 = 0
c) Sum of Moments about the base of the ladder = 0:
To find the forces exerted on the ladder, we need to take moments around the base of the ladder. This equation can be written as:
(f1 x a) + (weight of the ladder x (a/2)) - (f2 x b) = 0
- where a = 4.3 m (length of the ladder), b = 3.8 m (distance to the midpoint from the base)
Now, you can solve these equations to find the forces exerted on the ladder when the person is halfway up the ladder.
To find the forces exerted on the ladder when the person is halfway up, we can use the equations mentioned:
a) Sum Vertical Forces = 0
b) Sum Horizontal Forces = 0
c) Sum of Moments about the base of the ladder = 0
Let's start by labeling the forces and distances in the figure.
Let:
- f1 be the normal force exerted by the floor on the ladder
- f2 be the frictional force exerted by the floor on the ladder
- f3 be the normal force exerted by the wall on the ladder
- f4 be the weight of the ladder
- f5 be the weight of the person
- f6 be the force exerted by the person on the ladder
The length of the ladder is 4.3 m, so the halfway point is at 4.3 m / 2 = 2.15 m.
Now, let's apply the equations:
a) Sum Vertical Forces = 0:
f1 + f3 - f4 - f5 = 0
b) Sum Horizontal Forces = 0:
f2 + f6 = 0
c) Sum of Moments about the base of the ladder = 0:
- f5 * 2.15 + f1 * 4.3 - f3 * 4.3 = 0
We also know the weight of the ladder and the person:
f4 = 57.5 N
f5 = 85 kg * 9.8 m/s^2 = 833 N
Now, we have three equations with three unknowns (f1, f2, f3). We can solve them simultaneously to find the forces exerted on the ladder when the person is halfway up.