Laws of Motion -07- The Magnitude of Hinge Force

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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.

Transcript

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!

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