A single force with x-component Fₓ acts on a 500 g object as it moves along the x-axis. The object's acceleration graph aₓ versus t) is shown in FIGURE P5.30. Draw a graph of Fₓ versus t.

Video transcript

Hey, everyone in this problem, we're told that a net force with only A Y component fy is applied on a 1500 g metal block moving parallel to the Y axis. You were provided with an acceleration time graph of the block and were asked to sketch a force time graph. All right. So we're given this acceleration time graph. So we have time on the X axis. This Y acceleration on the Y axis time is given in seconds, acceleration in meters per second squared. And there's kind of three main points to look at. OK. So at two seconds, our acceleration is 0 m per second squared. At four seconds, our acceleration is 0.5 m per second squared. And at six seconds, our acceleration is 1 m per second squared and those are connected with a straight line because we have this linear relationship between acceleration and time. Now we're asked to sketch a force time graph for this block. So let's recall the relationship between force and acceleration. OK. New second law tells us that the net force net is going to be equal to the mass m multiplied by the acceleration. Well, we know the mass, we're told that the mass is equal to 1500 g. And we can write that in kilograms by dividing by 1000. So we have 1.5 kg. And then at any given time point, we can look at our graph find the corresponding acceleration that's gonna allow us to calculate the force. OK? Because we'll know the mass and the acceleration. So let's start, we're gonna draw a little table here and we're gonna fill in the values for those three points that we read the acceleration off of those three points where we have nice accelerations to read. Yes, we have the time and seconds, the Y acceleration in meters per second squared and then we're gonna have our net force and that net force is gonna be in the Y direction as well. All right. So we're drawing our little table here and we're gonna look at three time points at two seconds at four seconds and at six seconds now at two seconds, our acceleration is 0 m per second squared at four seconds. Our acceleration is 0.5 m per second squared. And at six seconds, our acceleration is 1 m per second square. So we move to our net force column for T equals two seconds. We have that acceleration of zero and so our net force is gonna be the mass 1.5 kg multiplied by the acceleration, 0 m per second squared, which gives us a net force of zero Noles we do the same for the next time point. OK. Our net force is gonna be the max 1.5 kg multiplied by the acceleration, 0.5 m per second squared, which gives us a net force of 0.75. No, that's at four seconds at T equals six seconds. We have an acceleration of one. So our net force is 1.5 kg multiplied by 1 m per second squared for a net force of 1.5 news. All right. So we have these three, we know that the relationship between the time and the acceleration is linear. That means that the relationship between time and the force is also gonna be linear. OK? Because of this Newton second long relationship. So if you scroll down and dry out this graph, we have time in seconds on the X axis, the net force in newtons on the Y axis at T equals two seconds. OK. Let's add some numbers here. We have two seconds, four seconds and six seconds. And then along the Y axis, we're gonna have 0.75 and 1.5. Those are numbers of interest there. All right. So at two seconds, we have a net force of zero nus, we add the 0.2 comma zero to our graph. At four seconds. We have a net force of 0.75. S add that to our graph. And at six seconds, we have a net force of 1.5 nodes. Again, add that to our graph and we can connect those with a straight line because we know that that's a linear relationship. OK. And we could have done points in between. We could have looked at three seconds and five seconds as well. But we really just needed those three points in order to get the overall picture of what's going on here. Ok. And so that's the graph of the force. Um And versus time. Thanks everyone for watching. I hope this video helped see you in the next one.