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18 Aunllo aboutil(olluclluatian € 372,* moving dawn the inclinc at consant Inclined ptane, wlth angle block moves 5,0 m ,ongthe Incling I+30 | What Is the 31 ...

Question

18 Aunllo aboutil(olluclluatian € 372,* moving dawn the inclinc at consant Inclined ptane, wlth angle block moves 5,0 m ,ongthe Incling I+30 | What Is the 31 14 A block on :74 Kclority The work done by the friction force % the tad oltbe block} ( Given sin 378 c0s37" 5.0 (Ak

18 Aunllo aboutil( olluclluatian € 372,* moving dawn the inclinc at consant Inclined ptane, wlth angle block moves 5,0 m ,ongthe Incling I+30 | What Is the 31 14 A block on :74 Kclority The work done by the friction force % the tad oltbe block} ( Given sin 378 c0s37" 5.0 (Ak



Answers

A $6.0-\mathrm{kg}$ block is pushed 8.0 $\mathrm{m}$ up a rough $37^{\circ}$ inclined plane by a horizontal force of 75 $\mathrm{N}$ . If the initial speed of the block is 2.2 $\mathrm{m} / \mathrm{s}$ up the plane and a constant kinetic friction force of 25 $\mathrm{N}$ opposes the motion, calculate $(a)$ the initial kinetic energy of the block; $(b)$ the work done by the $75-\mathrm{N}$ force; $(c)$ the work done by the friction force; $(d)$ the work done by gravity; (e) the work done by the normal force; $(f)$ the final kinetic energy of the block.

In this situation, we have given that a block is rest on a rough inclined plane which is at an angle of 30°. And we have given the frictional force on the blog, that is 10 Newton. We have to find the mass of this blog. So this is the inclined plane and there is a block on this inclined plane. Let the mass of this block is M. And I'm going to show the forces that is acting on this block. Let this angle is trita. So weight of this book is acting particularly downward, that is MG. And the component of this weight in this station is given by that is um the scientist er and in this direction this is equal to MG cost you to there is the normal force, this is equal to M. And the frictional forces acting, oppose it to this motion. This is equal to F. Now in the execution, we have given that the angle twitter is 30 degrees and we have given the value of Z. That is 10 m per second is square. And we have given the value of frictional force that is 10 Newton. Now we can say that it is given to us dead blockages at rest. So we can say that net force on the black bloc should because 20. So this is from here we considered MG scientist to minus frictional force that is F. Is equal to the zero. Now, put all the detention situations from here, we can see that this is M into turn into the sea sign 30 And this is equal to 10. So from here we can find the value of them. This will come out to be two kg, so this is the mass of the blog and they see that were answered. So we can say for that option is the correct choice. Thank you.

For this problem. On the topic of force and motion, we are told that a 2.5 kg block is addressed on a horizontal surface. A force F of magnitude six Newtons acts on the block horizontally. And a vertical force pr then applied to the block has shown in the figure. The coefficient of friction for the block and surface are U. S. 0.4 and U k 0.25 We want to find the magnitude of the frictional force acting on the block. If he has a magnitude of eight newtons, B, 10 newtons and c 12 newtons. Now we can choose X to be positive right words, and why it be positive upwards. And we can apply Newton's second law in the horizontal direction. We have the applied force F minus the frictional force. Little F. Is equal to M. A. In the vertical direction. We have P plus the normal force that the flow exerts on the block, minus the weight of the block. Mg was equal to zero. Since there's no net motion in the vertical election, we have F. Being six newtons and M 2.5 kg. And so for part A. If P is equal 28 newton's, then we can see that the noble force F. N. Is equal to 2.5 kg times 9.8 m per square second minus P, which is eight newton's. And so the normal force has magnitude 16.5 newtons. And so the static frictional force Fs max is equal to us times F. N, which is 6.6 newtons. And so this is larger than the six newton right would force so the block does not move. Which so let the acceleration be zero in the and into the first. For equations above, we get the frictional force F to equal to the blood force P, which is six newton's in part B. We have the applied force P. To be 10 newtons, which gives us the normal force F. N. To be 2.5 kg times 9.8 m per square second. And so the normal force and this is minus P, which is minus 10 m. So the noble force is 14.5 newtons. And the maximum static frictional force F. S. Max in this case, new S. Times F. N. Is 5.8 newtons. This is less than the six nutrient right would force. So the block block does move. So we're not dealing with static but we're dealing with kinetic friction. And so the kinetic frictional force F. K. Is equal to the coefficient of clinic fiction mu K times the normal force FM. Which gives us a frictional force of 3.6 newtons. For part C. We have the applied force p equal to 12 newtons. This gives us the normal force F. N. To be 12 0.5 newtons. And so the maximum static frictional force is equal to five newtons, which is less than the six newton Reitman force. And so again the block moves. And we have kinetic friction, and so the kinetic frictional force f. K, is equal to the coefficient of kinetic friction times This normal force FN, which gives us the frictional force, the 0.1 newtons.

So over here this is the figure that we are going to use for the difference. So this is a block and it is a fool by the courts that have my newsome and the direction 40 degrees with the horizontal. Okay. What do you live with the horizontal? And the 3.5 G. And forced me to be 15 newton. Okay, so this is this block have matched 3.5 kg. And this force had been used in many right. And one more thing which we have given that the conversations of kinetic friction with the block and the floor is zero point is like that. You don't want to have that. So we need to find first of all the friction force and calculate the magnitude of the force. And then the installation of the Bill of rights were very simple person in the first place. And what we can do each Uh there is envy for John one right. And one component of will be also the downward. So of course it will be in order to relax and have scientists. So this force will be converted into normal friction force. Will do nothing but MG plus F of scientific into a monkey, write to MGM in 3.5 G. Using 10 to 10 Plus 15 neutral into sign of 45 40 degree. Mhm. Right. And into Maybe this is 0.25. The frictional force that comes out to be 44 Newton over here. No, we were the next part. What we have is that we need to find the uh exploration on the blocks. Basically It's a lesson how we can find. We know that the net force in this direction is 15. Uh So Sorry, it will be 44 into 44 needle into this 0.25 as well. So it will be 44.4. So it will be 11 you denied or not. We need to find the experience and how we can find, you know that the forward exhalation equal to I mean to april two f minus of F of cost because they had posted a component of the gentleness of friction for So excellent. Even we have reported that 15, of Course, of 40° minutes of 11 upon this mass, 3.5. So this comes out to be I guess would you .14? Which for a second? Okay, so this will be our answer.

So we can first use Equation 8 31 and we can obtain that the change in thermal energy would be equal to the kinetic frictional force multiplied by the distance. We know that this is gonna be equal to 10 Newtons multiplied by 5.0 meters. So this is equaling 50 Jules. And then we're going to use a quite equation 78 In order to obtain that the work is equaling the force times the distance. This would be equal to 2.0 Newton's multiplied by 5.0 meters. This would be equal to 10 Jules and then we can say that again Equation 8 31 Ah would give us that the work is equaling the change in kinetic energy, plus the change in thermal energy. Sorry, plus the changing potential energy plus the plus the change in thermal energy and this would be equal to rather reconsidered. 10 jewels would be equal to 35 jewels, plus the change in thermal energy plus 50 50 jewels. And we can then say that the change in thermal energy sorry the change in potential energy would be equal to negative 75 jewels. So therefore we can say that the work done by gravity would be equal to the negative change and potential energy. This is equaling, of course. Positive. 75 jewels. This would be the work done by gravity. So our final answer, the work done by gravity is 75 jewels. That is the end of the solution. Thank you for watching.


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