The Magnitude of Hinge Force
The rod shown in figure has a mass of 3 kg and length 3 m. In equilibrium, find the hinge force (or its two components) acting on the rod and tension in the string. Take g = 10 m/s², sin 53° = 4/5, cos 53° = 3/5.
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00:00Hi friends, no matter whether it is Tuesday or Sunday, if you have a high goal in life,
00:06you must work hard every day to achieve it.
00:11We often see hinges on windows or doors.
00:14This time we will learn to calculate the magnitude of the hinge force.
00:20One end of the stick is connected to the hinge, while the other end is connected to a rope
00:24attached to the wall.
00:26What is the magnitude of the hinge force?
00:31Let's discuss it.
00:34As usual, we have to draw a free body diagram of this system.
00:40The centre of mass of the stick is in the middle of the stick.
00:44So the force of gravity will act from the centre of mass of the stick.
00:50The rope is tense because of the tension force of the rope.
00:55For the force at the hinge, we do not know the magnitude and direction of this force.
01:00However, we know that each force can be resolved into vector components, what if the hinge
01:05force has a horizontal component H and a vertical component V?
01:13Of all these forces, the direction of the tension force of the rope is not the same.
01:18We also have to resolve this force into component vectors.
01:24This stick is in equilibrium.
01:27This means that the resultant force acting on the stick is zero.
01:32For the resultant force in the horizontal direction, H minus T cosine 53 is equal to zero.
01:41For the resultant force in the vertical direction, V plus T sine 53 minus W is equal to zero.
01:50We already know the values of sine, cosine and W from the problem sheet.
01:58We have two equations with three unknown quantities.
02:01We need one more equation.
02:06We know that the stick does not rotate, so the torque acting on the stick is also equal
02:10to zero.
02:14Because the axis is a hinge, H and V do not have a moment arm.
02:18The moment arm is only owned by W and the vertical component of the rope tension.
02:26As before, just enter the values that have been listed on the problem sheet.
02:32This is an easy calculation, T is about 18.75 Newtons.
02:41Knowing the value of T, we can substitute this value into the previous equation.
02:48H is equal to 11.25 Newtons.
02:54And V is equal to 15 Newtons.
02:59H and V are components of the hinge force.
03:04The magnitude of the hinge force itself is the square root of H squared plus V squared.
03:12We can calculate this value using a calculator.
03:16F hinge is about 18.75 Newton.
03:22It turns out that the magnitude of the hinge force is exactly the same as the tension force
03:26of the rope.
03:29Happy learning everyone!