Question

machines изть ртор 1. A box of mass 10 kg on a horizontal rough surface 19 being pushed horizontally with P = 50 N, if the coefficient of static and kinetic friction are us = 0.5 and uk = 0.33 respectively, what is the state of motion of the box? A. Not moving, impending motion B. Not moving C. Moving D. Cannot be determined

Answer 1

Solution : That box has a mass of 10 kg Applied horizontal force is P=50N coefficient of static friction M = 0.5 coefficient of kinetic friction M = 0.33 Before we go to solve the problem we need some basic idea about Inpending Motion and moving criteria. Impending Motion : say, a box has weight "W" the static friction between box and surface is ds . The box is in rest initially. - FMR Now horizontal force Pis applied to cause movement. Ify-o Raw since the block is in rest FMR therefore at first it will slip to came I MW movement. Now the friction force "f" acts in the opposite of applying load. the box will remain in its initial position as long as pat But when pat then the box will start to slip. This initial motion is known as Impending Motion. In other words when. w

pincreases I also increases but is has a maximum or ultimate value; upto that value the box will remain in its rest Position. But when the applied load canals to the maximum static Friction then the box reaches at the verge of equilibrium system, And at the next moment applied force overcomes the static friction force to let the box slip or start the impending motion. Moring Cateria: After starting the initial motion there are still - a little amount of frictional force exists which oppose the horizontal TEMAR movement of box. As long as prfx Ifry=0; the box will keeps its R=w IR MER horizontal movement and it will be remained x = MkW in moving condition. Here Mr= kinetic friction Fk - kinetic friction Force P

According to our problem. p=50N P-GON w R=W . F = MR I c Fu=MAR W = mg e afyao W = 10x9,81 implies F = MgW W -98.1 N and fr=MW so, fs = MgXW Ак-Чехw f = 0.5*98.1 Ik = 0.33x98.1 fs = 49.05N x= 32.373N. So, px Ik so pofs 50N> 32.373N 50N > 49.05N therefore the box therefore impending will be moving Therefore the state of motion of the box will be © Moving Note: To start movement the box must needs to Start the impending motion at first. there fore ultimately the box will be moving since pits as well as P> Sk Answer) motion will start