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And experiencing anet (orce that is directed to the lell The magnitude of the force is constant The Asledis moving to the lelt specdof the sledisincreasingdecreasi...

Question

And experiencing anet (orce that is directed to the lell The magnitude of the force is constant The Asledis moving to the lelt specdof the sledisincreasingdecreasingconstantNoanswer text provided.

and experiencing anet (orce that is directed to the lell The magnitude of the force is constant The Asledis moving to the lelt specdof the sledis increasing decreasing constant Noanswer text provided.



Answers

T] After a certain distance $D$ has passed, the gravitational effect of Earth becomes quite negligible, so
we can approximate the force function by
$$
F(d)=\left\{\begin{array}{ll}{-\frac{m k}{d^{2}}} & {\text { if } d<D} \\ {10,000} & {\text { if } d \geq D}\end{array} \text { . Find the necessary condition }\right.
$$
$D$ such that the force function remains continuous.

In this problem, it is saying that a mass of three KZ is subjected to a constant force. And under this action of the constant force, speed of the object changes from two m per second to 3.5 m per second in 25 seconds. So let us say this is the body which has initial velocity two m per second, and finally it becomes 3.5 m per second. And uh in the problem, it is given that the direction of the body remains unchanged. That is motion of the body remains unchanged. So in the direction in which it was initially moving in the same direction, it was. It is finally moving. No, the time for this motion is 25 seconds. We have to determine magnitude and direction of the force applied under which this act under which this change has occurred. So we have to determine what is the value of f Most of the body is also mentioned in the problem, which is three kids. E. So what will be our approach to solve this problem first? With the help of the canna Matic parameters that in itself velocity. Final velocity and time. With the help of these three quantities first, we will calculate what is the acceleration of the body and then we will apply Newton's second law of motion to calculate the force. So what are the charismatics parameter given in this problem? Initial velocity is two m per second. Final velocity is 3.5 m per second. Time required to to do this to do this change is 25 seconds. And we have to find actually listen first. So recall the formulas that were discussed in can emit except er or motion in one dimension. That which formula relates these four parameters. So the formula that relates these four parameters is we is equals two, you plus A. In two G. So here the final velocity V is 3.5, which will be equals two. Initial velocity you plus actual reason that we have to find and time is 25 seconds. So from here, what we can say three point we can send that to in left hand side. So this will be 3.5 points to will be equals to 25 so 1.5 is equals to 25. A. Therefore acceleration will be equals to 1.5 divided by 25. So this will be approximately 0.6 m per second squared. As we can see that acceleration is positive. So it means that the acceleration has the same direction as that of the force as that of the initial velocity. Since we had earlier considered the velocity to be positive, it means that the direction of motion was considered to be positive. So here, if the exhilaration comes positive, it means that this exhilaration is in the direction of motion. Therefore acceleration is equals two point 06 m per second square and in the direction of motion. No. From Newton's second law of motion, we know that net force in vector form net force acting on the body is equals two massive body into acceleration of the body. So first we will calculate magnitude of the force as the direction of the force will be seen as that of the direction of acceleration, since acceleration is directed towards the direction of muslim, that is in which the initial or final velocity were present in the same direction acceleration was present. Therefore net force will also be existing, or the constant force that was applied on the body will be directed in the direction of motion. So here we have to make an effort to calculate the value of force or the magnitude of the force. So to calculate the magnitude, we will, we have to put the value of mass and magnitude of the acceleration. So what is the mass of the body? And the problem? It is mentioned as three KZ. And actually listen, we have just calculated what 0.6 So this will give 0.18 newton. Therefore, constant force was constant course was 0.18 new 10 acting in the direction of motion of the body. So this is the answer for this problem.

In this exercise have a constant force being applied over a protein. And we want to know if the acceleration of the protein increases decreases or stays constant as the Prodan speeds up. So, in order to solve this exercise first need to remember that the momentum of a massive particle congee written us and times v times Goma, the force the net force applied over the particle ISS. The derivative off P, with respected T and gover, is equal to one over the square root of one minus B squared overseas square, so it can calculate F as a derivative of P with respect to time. Explicitly. So what I'm gonna do is to write this as D DT of and V, divided by the square root of one minus B squared, oversee square. Okay, I'm gonna calculate this, and then I'm gonna isolate the acceleration DVD t ah, and see how it behaves as V increases. Okay, so let's differentiate this expression with respect to t. So using the multiplication rule first, I'm gonna just differentiate V so m DVD T and I'm gonna leave the denominator intact. Then I'm gonna leave V intact and different shades. The denominator. So m v. Times the derivative of one over the square root of one liners V squared over two square. And this is a rip. This derivative is now by the chain rule. Is there a video is 1/2 times one minus V squared overseas square to the three halves. That's the derivative of the square root times the derivative of what's inside the square root. And that's minus to V Oversee square time to derivative of the Okay, All that I did here was to apply the change room. So what we have is M DVD T. Okay, just isolating DVD T times one over the square root of one minus V squared over C squared times one. The two years gets a lot So one plus V square overseas square times one minus B squared overseas square. Okay, and I can simplify this further. So here we have. I am DVD tee times one over the square root of one minor G square over she square the first time the first term inside the square brackets I'm gonna multiply and divide by one minus V squared overseas square. So we have one minus b squared over. C squared over one minus B squared over C squared, plus B squared over. C squared over. One man is we squared overseas square. So these two here, cancel out and we're left with M DVD T times 1/1 minus the square over C squared to the three has. Okay, And this is the force, and the force is a constant half is just a constant number. So I'm gonna isolate DVD t. So have a It was DVD t. And this is if times one minus v squared over C squared to the three halves, divided by AM. Okay, so we found I'm sorry. We found an expression in general expression for the acceleration as a function of the speed and noticed that as the speed goes up, the acceleration goes down. Okay, because of this minus sign here. And for that reason, we can say that the acceleration decreases as the Prodan speed up. Okay, Okay. And this conclusive the exercise

Hi. In the given problems, this is the long rectangular loop whose length suppose it is early and it's worth it is supposed to be B The current passing through the loop is island means initially the current which was passing through this loop was I want is equal to one. I am Pierre. Yeah. So the force of repulsion between these two lens as the current in these lands will be in opposite direction. So force of repulsion between these two lands will be F is equal to new, not by four bikes into to Ivan. I do, divided by the gap between them which is equal to the width of the soil, which is B and multiplied by the length the total force acting between these two lands. And if you put the value of this current to be one ampere, this force here comes out to be new not by four by into two into one m peer into one MP are divided by B into lengths. So finally we can write. This is new, not by four pi into two l by B. Now if we increased the current in this loop, two tries of the initial value means if we make it well, three ampere, then the force of repulsion between the same arms F dash will be given by new not by four pi into two into three ampere into three MPR divided by wits and land into land. So here it comes out to be new, not by four by into two into nine l by B or we can say this F dash is equal to nine times of new note by four by into two l bitey Or finally, we can say the force of rebellion between these two arms is increased by nine times. And this is the answer for this given problem. Thank you.

All right, we know that the some of the forces equals mass times acceleration. So if we're calling this a constant, some of the forces, which I think is the assumption to be made in this question, then the only way for acceleration to be increasing is if the mass is decreasing. So perhaps you're pushing like dry ice which is evaporating um at a constant force, then the acceleration would increase because the mass of the dry ice gets lower due to evaporation. That is a good b a constant force results in no acceleration. A constant force results in no acceleration. Well, I know for one thing that if it's but I guess what we're going to have to do is we're gonna have to focus here on the uh some of the forces. If the constant force is not enough to overcome, um perhaps like the frictional force, then you can be pushing on, for example, a box not overcoming the friction force and the objects not gonna move. So it there's no acceleration. So um oh basically when it's counteracted by other forces, I'm going to write it down counteracted by other forces. That should be a deep thank you.


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