Suppose the woman in Figure 1 is 54 kg, and the board she is standing on has a 10 kg mass. What is the reading on each of the scales?
Solution: The woman in the above figure is 54 kg, and the board she is standing on has a 10 kg mass. We need to find the reading on each of the scales Step 1 What is Static equilibrium : Static equilibrium is a form of equilibrium that occurs when an object is at rest. “Static” refers to the object being motionless while “equilibrium” refers to the object either having no net forces acting upon it or having all of its net forces balanced. The above figure shows that the body will be in static equilibrium if the net force F= 0, The net torque acting on the body equal to zero as well as the body does not change its position with respect to time. Step 2 When a system is in equilibrium, the sum of clockwise moments is equal to the sum of Counterclockwise moments. They given the A 54 kg Woman of standing on has a 10 kg mass, Weighing scale 1 is 1.5 m Weighing scale 2 is (2m - 1.5m) = 0.5m away from a woman. Therefore reading of each scales is 0.5m This is static equilibrium because the net force on the object is zero. The two forces are equal in magnitude and opposite in direction, the resultant force in this case is zero. Step 3 The normal components can be calculated as follows. In the above figure woman weight is 54 kg on the standing of mass 10 kg. The weight of the woman is w = mg Where, w is the weight m is the mass g is the acceleration of the gravity 2 We know that g = 9.8 m/s 2 w = 54 kg ×9.8 m/s w = 529.2 N Normal components of women n = d 1 2 d 1d 2 1.5 m × 529.2 N = 2 n2 396.9 N Hence we need to find the value of n so we 1t as, n = w - n 1 2 n We already know the value of the above equation so we need to find the value 1, n1 529.2 N - 396.9 N 1 = 132.3 N Step 5 Next we need to find the weight of the board, w = mg Where, w is the weight m is the mass g is the acceleration of the gravity = 10 kg ×9.8 m/s 2 w = 9 8 N d w n = 1 2 d 1d 2 1 m × 98 N = 2 n = 49N 2 Hence we need to find the value of n so we get as1 n1 w - n2 n = 98 N - 49N 1 n1 49N Hence the resulting of the reading are n = (132.3 N + 49N) 1 n1= 181.3 N n2 (396.9 N + 49N) n = 445.9 N 2