One end of a string is fixed to a point A and the other end is fastened to a small object of weight 12 N. The object is pulled aside by a horizontal force F, until it is 0.6 m from the vertical through A. Find the magnitudes of the tension T in the string and the force F.
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00:00Hey guys, if you think Tuesday mornings suck, think about your competitors.
00:07They must be working hard even on Tuesday mornings to beat you.
00:12This is about Lamy's theorem.
00:14Three forces act simultaneously on the same object.
00:20Consider this question, a particle connected to a string is pulled by a force to the right.
00:25We are asked to calculate the magnitude of the tension force on the string and the external
00:29force.
00:34Let's discuss.
00:36There are several forces acting on the particle simultaneously.
00:40How about we draw a force-free diagram?
00:44The force of gravity is downward.
00:49The tension force on the string is in the direction of the string.
00:55And the external force is to the right.
01:00There are three forces acting on the same particle.
01:03The particle is in equilibrium.
01:06We can state that Lamy's theorem is valid.
01:12We need to determine the angle around the particle.
01:15The angle between the forces.
01:18Let's say this angle is theta.
01:23So the angle between gravity and the tension force on the string is 90 plus theta.
01:30The angle between gravity and the external force is of course 90 degrees.
01:36And the angle between the external force and the tension force on the string is 180 minus
01:42theta.
01:45Based on the Lamy's theorem, F over sin of 90 plus theta is equal to T over sin of 90
01:51degrees, which is equal to W over sin of 180 minus theta.
02:00In the trigonometric identity table, this value can be written as sine theta.
02:07And this value can be written as cosine theta.
02:13Sin of 90 degrees is 1, we have memoized this value.
02:20There is a theta quantity here, we have to calculate this value.
02:25If I'm not mistaken, the length of the hypotenuse is 0.75 meters.
02:32From here, sine theta is 0.45 over 0.75, about 0.6.
02:41For cosine theta, that value is 0.6 over 0.75, about 0.8.
02:51Now substitute this value into the previous equation.
02:57T is equal to 12 over 0.6, or 20 newtons.
03:03Because the weight of the particle is 12 newtons.
03:09One more thing, F over 0.8 is equal to 20.
03:14F is equal to 16 newtons.
03:19It seems that the Lamy's theorem can only be used when three forces act simultaneously
03:23on an object to form a force equilibrium.
03:28Happy learning everyone!