A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall. The rod is uniform and of weight w. If the rod is in equilibrium in the position shown in figure. Find:
(a) frictional force at A
(b) normal reaction at A
(c) normal reaction at B
(a) frictional force at A
(b) normal reaction at A
(c) normal reaction at B
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LearningTranscript
00:00Hi friends, enjoy your day. Have faith in your heart and the courage to make all your
00:07dreams come true. Why is a stick leaning against a wall not
00:12moving? This is what we will learn in this video.
00:18We will calculate the magnitude of each force acting on the stick.
00:26Let's go to the discussion sheet. An object will not move when there is no force
00:32at all. Is that true?
00:36We know that the stick is an object with mass. Objects with mass will be attracted to the
00:41earth's core. Then why is the object still not moving?
00:49We must know that when the resultant force acting on an object is zero, it is the same
00:53as there is no force. There must be another force on the stick.
01:01The stick does not penetrate the floor surface. There is a normal force N1.
01:09The stick does not penetrate the wall. There is also a normal force N2.
01:17It seems that the floor surface is rough. Based on the tendency of the direction of
01:22motion, the friction force will work towards the left.
01:27It turns out that it is true, for forces are working on the stick.
01:34The resultant force on the stick must be zero. For the vertical direction, N1-W equals zero.
01:44For the horizontal direction, N2-F1 equals zero.
01:51One more requirement that is often forgotten. The stick is also not rotating.
01:57The resultant torque is also equal to zero. We are free to choose the axis of rotation.
02:06Let's say the axis is 0.2 and the length of the stick is 2L.
02:15The moment arm of the gravity force is Lcos 60 degrees.
02:19The sine of the torque is negative because gravity tends to rotate the stick clockwise.
02:27The moment arm of N1 is 2Lcos 60 degrees. The sine of the torque is positive.
02:36The moment arm of the friction force is 2Lsin 60 degrees.
02:41The sine of the torque is negative.
02:46We have three equations with some unknown quantities.
02:51From the first equation, N1 is equal to the weight of the stick.
02:57From the second equation, the magnitude of the force F1 is equal to the force N2.
03:05Then we can substitute these two values into the third equation.
03:12I am sure we have memorized the sine of 60 degrees and the cosine of 60 degrees correctly.
03:20This equation can be written as root 3 N2 is equal to half W.
03:28Or N2 is equal to one sixth W root 3.
03:35Since the value of F1 is equal to N2, the value of F1 is also equal to one sixth W root 3.
03:45This is the value of all the forces acting on the stick that cause the stick to lean and not move at all.
03:51Happy learning everyone!