impulsive force model worksheet 4 answer key

More generally, an 'integral' is the sum of a large (infinite) number of very small (infinitesimal) quantities. This is an example of an 'integral,' which can often be thought of as the area under a curve. 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.

Impulsive force model worksheet 4 answer key