A 2.0 kg particle moving along the x-axis experiences the force shown in FIGURE EX9.22. The particle's velocity is 3.0 m/s at x = 0m . At what point on the x-axis does the particle have a turning point?

Video transcript

Hey, everyone. So this problem is working with the work energy theorem. Let's see what they're asking us. We have a 2.5 kg object subject to a position dependent force that's shown in this figure here. And it moves in a straight line on a horizontal friction list plane at the position X equals zero, were given the velocity of the object as minus four m per second and were asked to determine the position where the object reverses its direction. So the key here is to recognize two things. First, we know that when the object reverses its direction, it is momentarily at a zero speed. So right before it starts moving in the opposite direction, it actually has no speed. So we're going to write that as V F equals zero, we're given our initial speed And the problem here as -4 m/s. And we also have our mass. So I'll just note that from the problem mass is 2.5 kg we can also recall from the work energy theorem that the work is equal to our change in kinetic energy. Recall that our kinetic energy is given by one half MV squared. So delta K is going to be one half M V F squared minus one half MV I squared. So R V F is zero. So this whole term goes to zero. And so our delta K can plug in Our known values of mass 2.5 kg Initial speed -4 meters per second. That term squared, we come up with a change in kinetic energy Of -20 jewels. From here, we can recall that the work is equal to the area under the curve. So the work is the integral of the force. And so we know that our position dependent forces shown in this diagram. And we're looking for a distance in In position X where the object reverses its direction or where the kinetic energy is going to be equal to negative 20 jewels. For the way another way to look at that, we know we're moving in the negative X direction. So look at the magnitude we're looking for 20 jewels. So the area under the curve, we know each box here is two units or two jewels. And so we can work through this diagram that was given to us to find where we are when we hit 20. And so we'll count these up And see that when we get to four m, we are at 20 jewels. So that is the answer to this problem answer the, that's all we have for this one. See you in the next video.