![]() Stiff and bent-leg landings that produced the force vs. The reason is that rigid legs bring you to an abrupt stop, but bending your knees allows you to spread the landing out over a longer time which reduces the average and peak force applied to your legs. You naturally tend to bend your knees when landing after a jump, rather than keep your knees locked and your legs rigid. Now let’s use the Impulse-Momentum Theorem to calculate the fall speed and check that we get the same result. In the very first unit we used the kinematic equations to find the speed an object reaches after falling for a certain time. In that case we could simplify the change-in-momentum side by factoring out the mass and using standard notation for a changeĮither way, we see that changes in momentum require some non-zero net external force to be applied for some non-zero amount of time, which agrees with Newton’s First Law, but now for the first time we can actually analyze the forces on systems that are not in equilibrium. Notice that we have assumed the mass of the system did not change so we did not designate initial and final mass. The right side of the equation is the initial momentum subtracted from final momentum, also known as the change in momentum. The left side of the equation, average force multiplied by the collision time, is known as the impulse ( I). When the net external force on a system is not zero, then the system momentum will change according to the Impulse-Momentum Theorem: Overall, the center of mass velocity of the whole system does not change. ![]() This collision causes a leftward change in motion for Becky and a much smaller rightward change in motion for Sean and the author. Sitting in a wheeled chairs, Science Lab Technician Becky Kipperman (left) and Chemistry Professor Sean Breslin (right) push against one another while the author is attached to Sean in another chair, but not touching the floor. For example, the individual components of the larger systems are just smaller systems themselves, and those smaller systems certainly did experience changes in velocity. Now we would like to analyze systems that are not isolated, meaning they do feel a net external force. In the previous sections analyzed systems that were isolated so we knew that the total momentum of the system could not change.
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