In the figure, a horizontal force Fx of magnitude 20.0 N is...

In the figure, a horizontal force $F_x$ of magnitude 20.0 N is applied to a 3.10 kg book as the book slides a distance d = 0.44 m up a frictionless ramp at angle $\theta$ = 30°. (a) During the displacement, what is the net work done on the book by $F_x$, the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement? Use g=9.81 m/s².

Transcript

00:01 In this question, in the first part, we need to find out the work done, the network done by the book when it travels a distance t upon the inclined plane.

00:18 So this is quite easy.

00:20 So we have to find out the force of a horizontal force, a pha is active on the book.

00:28 So we need to find the parallel component of faa parallel to the inclined plane.

00:34 So f of a is going to be the parallel component is going to be cost theta because this angle is going to be 30 so f a cost 30 multiplied by d so we know the values of f a is going to be 20 this is going to be cost 30 multiplied by the distance is point nine this is going to be 15 .6 jules so this is the network done and we also need to find the gravitational force force which is going to be mg we know the mass of this is 2 .91 and the gravitational acceleration which is 9 .8 so we know the the gravitational force acting on the book which is 28 .6 newton and we also have to find the normal so to find the normal we have to resolve all the forces which are perpendicular to the plane acting on the book so we can see the component of the horizontal force is also acting on the book so we can see in this the parallel component is f cost theta and the perpendicular component is f sine theta so from this we know and we also have to resolve the weight so we need to resolve the weight so i will draw in another body diagram so this is the book and this is the weight acting vertically downwards so we have to resolve this into components a component perpendicular and the component parallel so the perpendicular component is going to be w cost theta and the parallel component is going to be w sine theta and so to find out the normal we'll grow another so this is our plane this is our book and we have to draw the foreselecting on it so the normal acts perpendicular to the plane and the other two forces are the first force is going to be w cost theta and the second force is going to be you can see in the above diagram it's going to be f sign theta f a sign teta so now so we can find out the normal normal is going to be equals to w cost theta theta is going to be 30 plus f a sign 30 so this is going to be, we have found out the weight which is 28 .6, 28 .6 cost 30.

04:33 And we know the force which is 20 newtons, 20 sine 30.

04:38 So the normal acting on the book is going to be, the normal is going to be 34 .8 newton.

04:51 So we have completed the part a and we have to see what we have to do in the part b...

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