Question

A uniform 6.0 kg ladder is leaning against a frictionless vertical wall, with which it makes a 15 ?angle. The coefficient of friction between ladder and ground is 0.26.

Can a 58 kg person climb to the top of the ladder without it slipping?

If so, how massive a person would make the ladder slip?

Answer 1

Given is:-

mass of the ladder m_l = 6 kg

Angle between vertical wall and the ladder is 15 degree

therefore the angle with horizontal is 90-15 = 75 degrees

The coefficient of the friction between ladder and the ground is = 0.26

Now,

The forces on the ladder is shown in the sketch below

with the force exerted by the (frictionless) wall horizontal. The person is up the ladder a fraction ? of its length. Equilibrium conditions require:

( Here, we used the horizontal force equation to find f, the torque equation to find F_wall and the vertical force equation to find N.)

For a person at the top of the ladder   and the coefficient for no slipping becomes

by plugging all the values we get

Therefore

a 58 kg person can easily climb to the top of the ladder without slipping.

Perosn whose mass is greater than 95.12kg would make the ladder slip