Question
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.
is the minimum force needed to get the ladder to move? The static coefficient of friction for all contact surfaces is 0.4.
Answers
bobpursley
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.
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.