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Two students each push a 30 kg box across the room. Student A applies a constant force of 30 N. Student B starts with a force of 40 N but gradually reduces the force due to fatigue. Given the force-versus-position graphs of the two students, at what position have both students done the same amount of work?(A) 2 m(B) 3 m(C) 4 m(D) 5 m

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Chapter 13

Practice Test 3

Section 1

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Hi. In the given problem, there is a box having a mass Of M is equal to 30 kg. It is being pulled by two students. Student A is applying a force on it. F. A. Is equal to 30 newton, and this force is constant and student B is applying a force on it. F. B. Which is initially Having a magnet Euro 14 Newton and then gradually it starts reducing. No. For this problem, we use the concept that work done is found by the area off force versus displacement occurred. Now the forced displacement girl for the two cases means for the force applied by student A and by student B is giving here in the problem like this. First of all, four student A. The force is constant and that force and the forces being represented over the Y axis, which is measured in newton. And the displacement means a position is being represented on the X axis and that is measured in nature. This constant force here is 30 newton. Now, the force applied by the student B was initially having um agreed Europe 14 Newton, after which it starts decreasing. And it is given like this here in the problem. So this is 14 U. Turn over here. Then if you look for the the stands here, at which these two curves intersect each other, this position is given us to meter. So we conclude that for a decline of force of 10 newton, This decline in the force applied by student B takes place or a displacement of two m. So, using unitary methods, suppose the work done by the two students becomes equal after a displacement of X. So up to this displacement of X. What will be the drop in the force applied by student be. We have to find this drop. So to find this, we will use unitary matters which says four, our distance of two m. The reduction in force is dan newton. So For a distance of one m, this reduction in the force applied by Student B will be 10 mountain by two m is this is five newton. So what a distance of X meter. This reduction will be five into X. Newton means here, the force will be reduced by five X. So remaining force after distance X. The remaining force applied by Student B will be 40 minus five X. So At this distance, if we look for the two areas, one Is that covered by Student eight. Here, this is this is a rectangle so we can see over our distance. X. Work done by the student mm is W. E. And that is given simply by the area of rectangle shown in green and that is X means land. And here this width, Which is 30. So we can see this is Turkey ex jews. Similarly work done by student B is W. B. And that will be given by the area so far, trapeze iem here, this is doctorate museum. This And the area of Trumpism is given by the summer of parallel sides. Here, the parallel side, this parallel site is measured to be 14 Newton And this parallel side will be measured to be 40 -5 x. And the distance between them is X. So here it becomes half into some of parallel sites, 40 plus 40 minus five X. Multiplied by distance between them which is X. So it comes out to be AT -5 X. Into X x two Jews. But as these two works are the same. So these 30 x. is equal to 80 -5 x Into X, divided by two, cancelling this X. And making a cross multiplication, we get 60 is equal to 80 minus five X. Or we can say five X equals to 80 minus 60 since this is 20. So This X comes out to be four metre means after moving four metre, the work done by both, the students will be equal. Hence, here, we can say our option. See is correct. Here. Thank you.

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