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Nevermind, I understand now 🙂
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Question 278 - EK Physics - Confusing
- Thread starter ilovemcat
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Someone PM'd me about this question, so I thought I'd include my response here incase anyone decided to search this up:
It's important to keep in mind what forces are acting on a system. In question 278, the mass is being held by the tension in the string (T3). The tension in T3 pulling UP, is exactly equal to the weight of the block pulling DOWN. These two forces balance. The tension in T3 in turn must be balanced by the tensions in T1 and T2. Because T3 is strictly a VERTICAL force, it is the vertical components of strings T1 and T2 that counter the tension in T3. More specifically: T1sin(theta) + T2sin(theta) = T3.
You also have to consider the horizontal components as well. Both T1 and T2 have a horizontal component. These are the only two forces acting in the horizontal direction (both opposing each other). Because the system is in equilibrium, these forces must balance also: T1cos(theta) = T2cos(theta)
Looking at the diagram, T2 has a slightly smaller angle than T1. For the above expression (in bold) to be valid, the magnitude of T2 must smaller than the magnitude of T1. This is because as the angle (theta) decreases, cos(theta) increases. Therefore, T1 > T2.
Choice D is wrong because T1 and T2 consist of a horizontal component (both of which must balance), PLUS the vertical components needed to balance T3. It's impossible for T1 + T2 to equal T3.
It's important to keep in mind what forces are acting on a system. In question 278, the mass is being held by the tension in the string (T3). The tension in T3 pulling UP, is exactly equal to the weight of the block pulling DOWN. These two forces balance. The tension in T3 in turn must be balanced by the tensions in T1 and T2. Because T3 is strictly a VERTICAL force, it is the vertical components of strings T1 and T2 that counter the tension in T3. More specifically: T1sin(theta) + T2sin(theta) = T3.
You also have to consider the horizontal components as well. Both T1 and T2 have a horizontal component. These are the only two forces acting in the horizontal direction (both opposing each other). Because the system is in equilibrium, these forces must balance also: T1cos(theta) = T2cos(theta)
Looking at the diagram, T2 has a slightly smaller angle than T1. For the above expression (in bold) to be valid, the magnitude of T2 must smaller than the magnitude of T1. This is because as the angle (theta) decreases, cos(theta) increases. Therefore, T1 > T2.
Choice D is wrong because T1 and T2 consist of a horizontal component (both of which must balance), PLUS the vertical components needed to balance T3. It's impossible for T1 + T2 to equal T3.
