An object experiences a force given by the graph below. What v...

Question

An object experiences a force given by the graph below. What value of Fmax would give an impulse of 6 N⋅s?

Accepted Answer

Hey guys, let's take a look at this problem. It's a pretty interesting one involving a force versus time graph like this. We know we're gonna have to calculate some areas of the curve. Let's check it out. We're told to find the value of F max so that we can get an impulse of six newton seconds. We actually already know the area under the curve is going to be so remember that your impulse equation is gonna be the area under the curve and that is actually equal to six newton seconds, where actually we're told what the answer is. So basically what happens is that the area that is between this red line here and the X axis. This is equals to six. We want to do is we want to figure out the value, this has to be in order to make this equation six. And basically what happens is this area that we calculate is going to have an expression, there's gonna have a variable and that's where F max is going to come from. Let's check this out. So basically what we can do is we can use these two formulas here for rectangles and triangles. Now this looks like a triangle. So we can do is we can actually break it up into two right triangles, where we can only use this equation one half base times height. If we break this into a right triangle. So I'm gonna do is I'm going to sort of split this right down the middle, so this is five milliseconds like this, and then we can use the equation one half base times height for both of them. One half base times height ear. What we're doing is we're using the base of our triangle is equal to the difference between five and eight, which is three milliseconds, the heights of this triangle, The H. Here is actually equal to the F. Max. And that's where sort of factors into our equation here. So I'm producing the right expression for this area because we know that the area under this curve has to be six. So what happened is I have two right triangles. So I'm going to use one half base times height twice. So this is going to be two times one half base times height. The two and the one half will cancel. Remember that we said the base is equal to three milliseconds here. So this is going to be 0.3 and the height of this triangle, we said it's going to be our F. Max. So basically what our equation turns out to be is 0.3 times F max is equal to six newton seconds. And we can do Is we can actually divide by the 0.003 to get f. max here. So you're gonna bring it to the other side and this F max has to be six divided by 0.3 And you're gonna get a 2000 newton F max. So basically what happens is you have this little spike here of this impulse graph. This F max is 2000, but it acts for a very short amount of time. Only about 60 milliseconds to deliver an impulse six newton seconds. Alright, so that's it for this one guys, let me know if you have any questions.

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