A heavy metal beam AB of mass 25kg is supported at it's end .The beam carries a mass of 150kg at a distance of 0.75m from end A .If the beam is 2m long determine the thrust at A and B.
Answer
Answer
To determine the thrust at point A and B, we need to consider the forces acting on the beam. Since the beam is supported at point A, there will be an upward thrust at point A (T_a) and a downward thrust at point B (T_b). Additionally, there will be the weight of the beam and the weight of the mass hanging from it acting on the beam.
First, let's calculate the weight of the beam (W_beam). The weight is given by the formula:
W_beam = mass × gravitational acceleration
W_beam = 25 kg × 9.8 m/s^2 (taking the gravitational acceleration as 9.8 m/s^2)
W_beam = 245 N
Next, let's calculate the weight of the hanging mass (W_mass). The weight is given by the same formula:
W_mass = mass × gravitational acceleration
W_mass = 150 kg × 9.8 m/s^2
W_mass = 1470 N
Now, let's calculate the distances of the weight and the mass from point A. The distance of the weight from point A is 2 m (the length of the beam), and the distance of the mass from point A is 0.75 m.
To determine the thrust at point A (T_a), we can calculate the moment (torque) about point A and set it equal to zero. The moment is given by the formula:
Moment = (Force × Distance)
The clockwise moments acting are the weight of the beam and the mass multiplied by their respective distances from point A. The anticlockwise moments acting are the thrust at point A (T_a) multiplied by its distance from point A (which is zero since it acts at point A) and the thrust at point B (T_b) multiplied by its distance from point A (which is 2 m – 0.75 m = 1.25 m).
Setting the moment equal to zero:
(Weight of the beam × Distance of the beam) + (Weight of the mass × Distance of the mass) - (Thrust at A × Distance of A) - (Thrust at B × Distance of B) = 0
(245 N × 2 m) + (1470 N × 0.75 m) - (T_a × 0) - (T_b × 1.25 m) = 0
490 Nm + 1102.5 Nm - 0 - 1.25T_b = 0
1592.5 Nm - 1.25T_b = 0
1.25T_b = 1592.5 Nm
T_b = 1274 N
Now that we have the value for thrust at point B (T_b), we can substitute it back into the equation to find the thrust at point A (T_a):
1.25T_b - 1592.5 Nm = 0
1.25T_a - 1592.5 Nm = 0
1.25T_a = 1592.5 Nm
T_a = 1274 N
Therefore, the thrust at point A is 1274 N and the thrust at point B is 1274 N.