Finding Impulse using Momentum Principle - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-23T18:01:25Z https://physics.stackexchange.com/feeds/question/276922 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/276922 0 Finding Impulse using Momentum Principle Chris Loonam https://physics.stackexchange.com/users/99359 2016-08-28T21:59:24Z 2018-01-21T04:28:35Z <p>I am currently doing my Physics homework and am stuck on a problem that is giving me an issue.</p> <blockquote> <p>A tennis ball has a mass of 0.057 kg. A professional tennis player hits the ball hard enough to give it a speed of 46 m/s (about 103 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (46 m/s). As indicated in the diagram below, high-speed photography shows that the ball is crushed about d = 2.7 cm at the instant when its speed is momentarily zero, before rebounding.</p> <p><a href="https://i.stack.imgur.com/qsDirs.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qsDirs.jpg" alt="image"></a></p> <p>Making the very rough approximation that the large force that the wall exerts on the ball is approximately constant during contact, determine the approximate magnitude of this force.</p> </blockquote> <p>After solving a very similar problem correctly, I took the following approach to solve it.</p> <p>$$|\vec{v_{avg}}|=\frac{46}{2}=23 \frac{m}{s}$$ This is the average velocity from the time that the ball first makes contact with the wall until it comes to rest, and this answer was marked as correct. </p> <p>The next step I took was to find the time it took from first contact with the wall until the ball came to rest. The question this was intended to answer was </p> <blockquote> <p>How much time elapses between first contact with the wall, and coming to a stop?</p> </blockquote> <p>$$t=\frac{|\vec{r}|}{|\vec{v_{avg}}|}=\frac{0.027 m}{23 \frac{m}{s}}=.0012\, s$$ However, this answer was marked incorrect, along with my answer that followed which found the total force exerted on the ball by the wall using this time.</p> <p>$$\Delta\vec{p}=\vec{F_{net}}\Delta t$$ $$|\vec{F_{net}}|=\frac{\Delta|\vec{p}|}{\Delta t}=\frac{2.622 \frac{kgm}{s}}{.0012\,s}=2185\,N$$</p> <p>Where did I go wrong in solving this problem?</p> https://physics.stackexchange.com/questions/276922/-/381108#381108 1 Answer by Atharva Kulkarni for Finding Impulse using Momentum Principle Atharva Kulkarni https://physics.stackexchange.com/users/176767 2018-01-20T07:56:33Z 2018-01-21T04:28:35Z <p><em>Edited after the mistake was pointed out by Ben51 :-</em></p> <p>The time can be found out by using the equation $\vec{s}= \vec{u}t + \frac{1}{2}\vec{a}t^2$ where $s$ is displacement in time $t$, $u$ is the initial velocity and $a$ is acceleration :- $$0.027=46t - \frac{1}{2}at^2 ; a=\frac{46}{t}$$ Therefore $$0.027=46t - 23t$$ Thus $$t=\frac{0.027}{23}$$ So the answer is coming out to be the same.</p>