A 2.0 kg object is moving to the right with a speed of when it experiences the force shown in FIGURE EX11.9. What are the object's speed and direction after the force ends?

Question

Graph showing force vs. time for a 2.0 kg object experiencing variable force.

Accepted Answer

Hey everyone. So this problem is working with the impulse momentum theory. Let's see what it's asking us given a 1.8 kg block with an initial speed of one m per second towards the right, determine the final speed and direction of the block. Once the force as shown in the figure below is removed, assume that there are no other forces acting on the object during this time and neglect any effects of air resistance. Our multiple choice answers here are a 0.71 m per second. B 0.81 m per second. C 0.62 m per second or D 0.52 m per second. OK. So the key to this problem is going to be recalling our impulse momentum theory which states that our final impulse or sorry, our final momentum is equal to our initial momentum plus our impulse where momentum he is given by mass multiplied by velocity and our impulse is equal to the integral of our force with respect to time. So the integral with re with sorry, the integral of force with respect to time. The integral is another way of saying the area under the curve. So we are given this graph of force on the Y axis time on the X axis. And so the area of this curve is going to be equal to our impulse. And so this is a trapezoid shape. So we can recall that the area of a trapezoid is given by A plus B divided by two multiplied by H. In this case, A and B are going to be our, the sides in our direction. And age is going to be the height in the Y direction. So we have 0.3 seconds plus 0.22 seconds divided by two, multiplied by a force of negative two nus. We plug that in and we get an impulse of ze- negative 0.52 newton seconds. And now we can use our momentum equation where momentum is equal to mass multiplied by velocity in our impulse momentum theorem to solve four. Our final philosophy. So that looks like the mass of the block multiplied by the final philosophy of the block is equal to the mass of the block multiplied by the initial velocity of the block plus our impulse. We can isolate our final velocity by dividing both sides by the mass of the block plugging. In our known values. The mass of the block was given to us in the problem as 1.8 kg. Our initial speed was given as one m per second. And then our impulse we just saw for is negative 0.52 Newton seconds. And then all of that divided by 1.8 kg again. So that's the, put that in for the final velocity of the block and we get 0.71 m per second. So that is the answer to this problem. And that aligns with answer choice A so that's all we have for this one. We'll see you in the next video.

A 2.0 kg object is moving to the right with a speed of when it experiences the force shown in FIGURE EX11.9. What are the object's speed and direction after the force ends?

Verified Solution

Key Concepts

Newton's Second Law of Motion

Impulse and Momentum

Area Under the Force-Time Graph