Calculating Upward Contact Forces of Uniform Ladder

[m3trj]

I found the following question in a textbook:



Two men are carrying a uniform ladder of length 12m and weight 250N. One man holds the ladder 2.0m from the front end and the other man is 1.0m from the back of the ladder.

Calculate the upward contact forces that each man exerts on the ladder.



The answer section in the textbook says the forces are 110N and 140N. But how do you go about calculating that? I really need an explanation as I just don't understand. I can see the forces add up to 250N, but I'm not sure how to calculate each force. Maybe I'm just dumb.

Any help would be greatly appreciated.

 

[arildno]

The moments of forces must cancel about anyone point as well.
Let us call the man near the front "A", who exerts a force $$F_{A}$$ on the ladder a distance 4m from the centre of the ladder.
Let us call the man near the front "B", who exerts a force $$F_{B}$$ on the ladder a distance 5m from the centre of the ladder.
Thus, we must have:
$$4F_{A}-5F_{B}=0\to{F}_{A}=\frac{5}{4}F_{B}$$

We also have that the sum of forces acting on the ladder must be zero:
$$F_{A}+F_{B}-250=0$$
Thus, $$\frac{9}{4}F_{B}=250\to{F}_{B}=\frac{1000}{9}=111.111...\approx110$$

Got it?

 

[thepatientmental]

Hello,

First of all, don't worry, you are not dumb! Calculating forces can be tricky and it takes practice to fully understand it.

Let's break down the problem step by step:

1. Draw a free body diagram: This is a diagram that shows all the forces acting on an object. In this case, the ladder is the object and we need to show the forces acting on it. Draw a straight line to represent the ladder and label the front and back ends as F1 and F2 respectively. Also, label the weight of the ladder (250N) acting downwards at the center of the ladder.

2. Identify the forces: In this problem, there are two forces acting on the ladder - the weight of the ladder (250N) and the upward contact forces exerted by the two men. The force exerted by the man at the front of the ladder (F1) is directed upwards and the force exerted by the man at the back of the ladder (F2) is also directed upwards.

3. Apply Newton's Second Law: This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the ladder is not accelerating, so the net force acting on it is zero. This means that the sum of all the forces acting on the ladder must be equal to zero.

4. Set up equations: We can set up two equations to represent the forces acting on the ladder - one for the x-direction and one for the y-direction. In the x-direction, the only force acting is F1, so the equation is F1 = 0. In the y-direction, the equation is F1 + F2 - 250N = 0.

5. Solve for the unknowns: We have two equations and two unknowns (F1 and F2). We can solve for F1 in the first equation and substitute it into the second equation. This gives us F2 - 250N = 0. Rearranging the equation, we get F2 = 250N. This means that the force exerted by the man at the back of the ladder (F2) is equal to 250N.

6. Substitute back: Now that we know the value of F2, we can substitute it back into the first equation to solve for F1. This gives us F1 = 0. This means that the force exerted