Vectors in Component Form - General Physics - Solved Past Paper, Exams of Physics

Download Vectors in Component Form - General Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! 3. (30 pts) Two farm hands attempt to pull a stubborn mule. One of the hands pulls with a force of 80 N at 75◦ north of west. The other hand pulls with a force of 120 N at 60◦ north of east. The mule pulls due south with a force Fm such that the sum of all three forces is zero (and hence the tug-of-war is currently a stale-mate). a) (10 pts) Make a rough sketch of these three vectors on a set (or sets) of axes. 80 N 160 N Fm 75o 60o b) (10 pts) Write the each of the vectors in component form using î for east and ĵ for north. Note that at this point you don’t (yet) know the magnitude of the mule’s force, so just use Fm rather than a number. Farm hand 1: −80 cos(75) î + 80 sin(75) ĵ = −20.7 î + 77.2 ĵ N Farm hand 2: 120 cos(60) î + 120 sin(60) ĵ = 60 î + 103.9 ĵ N Mule: −Fm ĵ N c) (10 pts) Work out the force with which the mule pulls, Fm, by setting the sum of the three vectors to zero. If you did this correctly, you’d find that it doesn’t actually work. The x-components of the two farm hand forces do not sum to zero. Therefore, the mule must be pulling in a direction other than due south. This complication was not intentional, thus I gave everyone 5 points for this problem. The remaining 5 points were awarded based on your attempt to sum the vectors, or at least the y-components. The actual answer (disregarding the equilibrium condition specified at the top of the page) works like this, assuming the mule pulls in some direction with force Fm: (−20.7 î + 77.3 ĵ) + (60 î + 103.9 ĵ) + ~Fm = 0 ~Fm = −39.3 î− 181.2 ĵ N The biggest problem with the answers here was a lack of units. The second most common problem was not actually solving for ~Fm after correctly setting things up.