A 53 kg box is being pushed a distance of 60 m across the...

A 53-kg box is being pushed a distance of 6.0 m across the floor by a force whose magnitude is 167 N. The force is parallel to the displacement of the box. The coefficient of kinetic friction is 0.22. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force.

Transcript

00:01 In this given problem, over a rough surface, there is a box, a force is acting on it towards right, capital f.

00:16 And this applied force is 167 newton mass of the box, that is m is equal to 57 kilogram.

00:35 Kilogram under the influence of this applied force the box moves a distance s is equal to 6 .1 meter now as the surface is rough so when the box will be moving towards right there will be a force of friction between the box and the horizontal surface and this force of friction will be given by mu k coefficient of kinetic friction mu k times the normal reaction here if the weight of the block is m g which is acting vertically downward on this surface then the surface will be applying a normal reaction on the box n and this n will be equal to m g so here it will be mu k times n or we can say mu k times m g so ultimately we see and yeah of course mu k the value of mu k is 0 .20.

01:50 Here we see there are the four forces acting on this box at the moment.

02:09 Number one applied force capital f 167 newton number two force of friction small f mu k times m g number three weight of the box or we can say gravitational force acting on the box w is equal to m g and finally normal reaction of the surface on the box is n but as per newton's third law of motion for every action there is an equal and opposite reaction so this is also equal to m g now we have to find work done by all these four forces so first of all using the expression for the work done as f s plus theta so if theta is 90 degree means force and displacement if they are perpendicular to each other.

03:35 Then as we know the value of cost 90 is zero so work done will be zero means no work will be done by those forces which act perpendicular to the direction of motion.

03:49 Hence we conclude here no work will be done by the gravitational force means by the weight of the box and by the normal reaction.

04:22 Out of the four forces, the two forces are doing no work.

04:26 Now, work done by the applied force that will be given by wf, subscript capital f.

04:44 This is f as cos zero degree because the direction of the displacement is same as that of the force.

04:53 So that is zero degree...

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