A uniform beam, WX, of length 90 cm and weight 50N is suspended on a pivot, 35 cm from W. It is kept in equilibrum by a means of forces T and 20N applied at...

Answer Details

To solve this problem, we need to use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point. In this problem, we can choose the pivot point as the point about which we will calculate the moments.

Let's start by calculating the clockwise moments. The weight of the beam, 50N, acts at the center of gravity of the beam, which is at a distance of 45 cm from the pivot point. Therefore, the clockwise moment due to the weight of the beam is:

50N x 45cm = 2250 Ncm

Next, let's calculate the anticlockwise moments. The force T acts at point Y, which is 10 cm from the pivot point. Therefore, the anticlockwise moment due to the force T is:

T x 10cm

Similarly, the force of 20N acts at point Z, which is also 10 cm from the pivot point. Therefore, the anticlockwise moment due to the force of 20N is:

20N x 10cm = 200 Ncm

Since the beam is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments. Therefore, we have:

2250 Ncm = T x 10cm + 200 Ncm

Simplifying this equation, we get:

T = (2250 Ncm - 200 Ncm)/10cm = 205N

Therefore, the value of T is 205N.

In summary, we used the principle of moments to calculate the value of T. We chose the pivot point as the point about which we calculated the moments. We calculated the clockwise moment due to the weight of the beam and the anticlockwise moments due to the forces at points Y and Z. We then equated the sum of the clockwise moments to the sum of the anticlockwise moments and solved for T. The answer is T = 205N.