A 7 m ladder weighing 250 N is being pushed by force F AT bottom What
is the minimum force needed to get the ladder to move? The static coefficient of friction for all contact surfaces is 0.4.
draw a digram. Notice on the wall, there is a horizontal force H1 into the wall, and a friction force on the wall downward, and some component of weight at vertically downward (V1)
At the base, there is a vertical force (v2), a component of weight, a horizontal pushing F, and a friction force opposing F.
Now you have several equilibrium equations you can write.
1) sum of vertical forces= 250
V1+V2=250
2) Sum of horizontal forces = zero
F-frictionbase- H1=0
3) Now write a moment equation about any point, I choose the center of the ladder. Assume the ladder makes an angle theta with the floor.
(F-frictionbase)7/2 SinTheta-(V2-frictionupwall)7/2 * cosTheta=0
Now, unknowns: friction base is a function of theta and V1. Frictionwallup is a function of H1, theta. V2 is a function of V1
So I see three equations, unknowns H2, V1, F so you should get an equation in terms perhaps of theta. I didn't work this out, but will be happy to check your work, but I am thinking it well be messy, so be careful.
To determine the minimum force needed to get the ladder to move, we need to consider the forces acting on the ladder. In this case, the main force to consider is the force of friction.
Step 1: Calculate the maximum force of friction.
The formula for calculating the maximum force of friction is:
Maximum Force of Friction = static coefficient of friction * normal force
In this case, the static coefficient of friction is given as 0.4 and the normal force is equal to the weight of the ladder, which is 250 N. To calculate the maximum force of friction, multiply the static coefficient of friction by the weight of the ladder:
Maximum Force of Friction = 0.4 * 250 N = 100 N
Step 2: Determine the force needed to overcome static friction.
To get the ladder to move, we need to apply a force that exceeds the force of static friction. The force needed to overcome static friction is equal to the maximum force of friction.
In this case, the force needed to overcome static friction is 100 N.
Therefore, the minimum force needed to get the ladder to move is 100 N.