When two billiard balls collide, in which direction would they travel after the collision? If a meteorite hits the earth, why does the earth remain in its orbit? When two cars collide with each other, why is one of the cars more damaged than the other? We will find that to answer such questions, new concepts must be introduced.Ĭonsider the situation where two bodies collide with each other. During the collision, each body exerts a force on the other. This force is called an impulsive force, because it acts for a short period of time compared to the whole motion of the objects, and its value is usually large. To solve collision problems by using Newton’s second law, it is required to know the exact form of the impulsive forces. Because these forces are complex functions of the collision time, it is difficult to find their exact form and would make it difficult to use Newton’s second law to solve such problems. Thus, new concepts known as momentum and impulse were introduced. These concepts enable us to analyze problems that involve collisions, as well as many other problems. The law of conservation of momentum is especially used in analyzing collisions and is applied immediately before and immediately after the collision. Therefore, it is not necessary to know the exact form of the impulsive forces, which makes the problem easy to analyze. Next, we will discuss and verify the concepts of momentum and impulse, and the law of conservation of momentum. The linear momentum (or quantity of motion as was called by Newton) of a particle of mass m is a vector quantity defined asĪs discussed previously, when two bodies collide, they exert large forces on one another (during the time of the collision) called impulsive forces. These forces are very large such that any other forces ( \(\mathrm \) (see Fig. The integral of impulse is written F xdt, where the integral sign is a distorted "S" meaning "sum" and the " dt " stands for "extremely small (infinitesimal) time interval.Find the torque on the block about (a) the origin (b) point A.Ī conical pendulum of mass m and length L is in uniform circular motion with a velocity v (see Fig. More generally, an "integral" is the sum of a large (infinite) number of very small (infinitesimal) quantities. (Note that a kgm/s is equivalent to a Ns). This is an example of an "integral," which can often be thought of as the area under a curve. Impulsive Forces And Momentum Worksheet 2 Answers - Squarespace. We're approximating the area under the curve by a bunch of rectangles, but if the little Δ t 's are small enough that the force isn't changing much during that short time interval, the total area of our rectangles is approximately equal to the area under the curve. We can continue through the entire collision with the spring, and we see that the total area under the curve is equal to the total impulse (and the total change in the momentum, which is the sum of all the changes to the momentum). In the next time interval Δ t 2, we can again represent the impulse (and the change in momentum) as the area of the next rectangle shown on the diagram. So the area of the rectangle is equal to the impulse during Δ t 1 and also equal to the change in momentum Δ p x1 during that short time interval. But F x1 Δ t 1 can be thought of as the area of a rectangle shown on the diagram, whose base is Δ t 1 and height is F x1. The small impulse F x1 Δ t 1 makes a small change Δ p x1 in the momentum. In the first short time interval Δ t 1, the spring is only slightly compressed, and the force F x1 on the cart is small. F How would you expect these values to compare?įinding Impulse Using Area Under the Curve There is a more accurate way to determine the actual impulse on the cart.
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