FRICTION ON INCLINED PLANE AND LADDER FRICTION

CIVIL ENGINEERING DEPARTMENT MGITER,NAVSARI. B.E. – II, SEM- III PRESENTED BY: group 8 SR.NO. NAME ENROLLMENT NO. 1 BAGHEL POOJA R. 130330106007 2 CHAVHAN TRUSHNA H. 130330106019 3 DESMUKH DIVYA G. 130330106029 4 PARMAR HINA M. 130330106059 GUIDED BY:- PREETI VARMA CIVIL ENGINEERING DEPARTMENT MGITER,NAVSARI.

Contents: FRICTION ON INCLINED PLANE LADDER FRICTION

Friction on inclined planes If a particle of mass m kg rests on an inclined plane of angle θ°, the forces acting will be: Normal Reaction R θ Friction Fr Friction Weight = mg Weight Normal Reaction To solve problems involving inclined planes, it is easier to resolve parallel and perpendicular to the plane.

When the particle is just on the point of slipping:- Resultant force is zero θ Fr R mg i j In limiting equilibrium

So the coefficient of friction is dependent only on the angle of the slope. If we know the angle at which the particle just starts to slip, we can use this to calculate the coefficient of friction. This is particularly useful when modelling as we can do a simple experiment to estimate a value for μ.

Particle just on point of slipping so EXAMPLE : A block of mass 3kg is placed on a rough horizontal table. The table is gradually tilted until the particle begins to slip. The block is on the point of slipping when the table is inclined at an angle of 41o to the horizontal. Find the coefficient of friction. 41o 3g R Fr Particle just on point of slipping so

Find the magnitude of the friction force on the particle. EXAMPLE: A particle of mass 10kg is at rest on a rough plane inclined at 30o to the horizontal. A horizontal force of magnitude 10N acts on the particle. Find the magnitude of the friction force on the particle. The coefficient of friction between the particle and the slope is m. Find an inequality that m must satisfy. 30o 10g N R Fr 10N

(a) (b) The friction inequality states

The ladder is a device for climbing or scaling on the roofs or walls. LADDER FRICTION:- The ladder is a device for climbing or scaling on the roofs or walls. It is made of wood or iron.

There are two long pieces in the ladder to which many small cross pieces called rugs are connected at equal distances to work as steps. The necessary and sufficient conditions of equilibrium for the ladder are:   ΣFx =0               Σ Fy =0                Σ Mi =0                                                                                                                                                                    Ladder friction

FORCES ACTING ON THE LADDER WL = Self weight of ladder through c.g. of ladder Wm = Weight of man standing on ladder Rf = Reaction by the floor on the ladder Ff = Friction force between ladder and floor Rw = Reaction by wall on the ladder Fw = Friction force between ladder and wall.

As the upper end of the ladder tends to slip downwards, therefore friction force between wall and ladder will be upwards. Similarly, as the lower end of the ladder tends to slip away from the wall, therefore the force of friction between floor and ladder will be towards the wall.

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