A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (a) Find the maximum net force on this cart. When does this maximum force occur?

Video transcript

Hey everyone today, we're dealing with the trolley. And this trolley which weighs 3.6 kg is accelerating in a straight line in the X direction. Now the acceleration of the trolley has been plotted on the graph below as a function of time. And we're being asked to determine the maximum net force, maximum net force on the trolley as well as the time when the maximum forces experienced. Excuse me. So to get a group of this before moving on, when dealing with blank versus time graphs, be a position or velocity or acceleration. It's very important to deduce or analyze the areas under the graph because they analyze or they represent very important quantities. So, through dimensional analysis, right through dimensional analysis, because we're dealing with meters. So we have uh meters and we have time or meters per second squared or acceleration as our Y axis and we have time as our X axis. If we were to find an area underneath the graph, it would be the X axis, times the y axis. Let's say right, let's just take within this small rectangle, it would be the acceleration times the time travel, which means meters per second squared into the time travel, let's just say seconds. Well, our second will cancel out and we'll be left with meters per second, which means that the area under acceleration versus time graph will represent the velocity. However, we don't need velocity in this question. We're only being asked to find the maximum net force and we can do that using Newton's second law which states that force net is equal to mass into acceleration. So we have no place for velocity. So it's not important but it's good just to make sure that we don't need to use velocity here. So if we want to find where the maximum net forces, Right? So let's write that out here and let's write this in blue. I feel it will be a little easier if we want the maximum net force. Well, the mass can't change, which means we need to find where we have the most acceleration. So acceleration is max that from the graph, we can see that the maximum acceleration Is at the beginning at Time zero. Right? That is the point of highest acceleration that happens at time is equal to zero. So, plugging that in Our mass is defined as 3.6 kg. And the maximum acceleration is 6.0 m per second squared, which gives us a final answer of 21.6 Newtons at times equal to zero or answer choice. D. I hope this helps. And I look forward to seeing you all in the next one