(11%) Problem 5: A uniform stationary ladder of length L = 2.7 m and mass M = 11 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.45. The ladder makes an angle θ = 51° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base. show answer No Attempt 33% Part (a) Find the magnitude of the normal force N, in newtons, exerted by the floor on the ladder.

970.2 N

Explanation:

We are given that

Length of ladder=2.7 m

Mass,M=11 kg

Coefficient of friction=

Mass of painter=8M

Distance from base=d

We have to find the magnitude of the normal force exerted by the floor on the ladder.

Normal force exerted by floor on the ladder=

Where

Normal force exerted by floor on the ladder=

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.