Question

If man is balanced with a system, find Tension, reading of the weighing machine.

Answer 1

Hint In order to understand the system, split the system into two parts and draw the free body diagram along with the forces. Solve the tension equations and arrive at the reading of the weighing machine if the person pulls the rope.

Complete Step By Step Solution
Let the tension applied on the rope be T. Now, the mass of the man and the mass of the box are the downward force acting on the whole system, assuming that the weight of the machine is negligible. There are two upward forces of T acting on the rope. Draw the FBD of the given scenario.


From the above image you can see the 2 systems, one is the box and the other is the man. Now, let us write the force equations for man system and box system separately.
Let W be the reading measurement of the man inside the box, now
\[T + W - (50 \times g) = 0\](considering Man system)
\[T + W - 500 = 0\](Taking g as \[10m/{s^2}\]) ---------1
Now, let us write the force equations for the second system, that is the box.
\[T - W - (20 \times g) = 0\]
\[T - W - 200 = 0\]---------2
Adding equation 1 and 2 , we cancel out the W term
\[2T - 700 = 0\]
\[T = 350N\]
Now that we have found out the tension of the rope, we can substitute in any of the equations to find the reading of the weighing machine. By substituting in equation 1, we get
\[350 + W - 500 = 0\]
\[W = 150N\]
Note: Weight is given in Newton’s, To convert Newton’s into kilograms , divide by g value
g value is \[10m/{s^2}\]
\[W = 15kg\]

Thus the weight reading on the weighing machine is \[15kg\]

Note
In mechanical terms, tension is defined as the pulling force that are transmitted by a string, cable or wire, etc., to an object axially. Major example of application of tension is the pulley system.