A borad, 3m long, is hinged at point a and is supported by a vertical rope at point b, 2m from a. A boy weighing 200 N stands at the end of the board at point c. Neglecting the weight of the board, calculate the force on the rope.
To calculate the force on the rope, we need to find the torque acting on the board caused by the weight of the boy.
1. The weight of the boy is given as 200 N. We can assume this force acts at the center of mass of the boy, which is at point c.
2. The torque caused by the weight of the boy is equal to the force multiplied by the perpendicular distance from the point of rotation (hinge) to the force. In this case, the distance is 3m (the length of the board) - 2m (the distance from the hinge to the point where the rope is attached) = 1m.
3. The torque (τ) is calculated using the formula: τ = force × distance. So, τ = 200 N × 1m = 200 Nm.
4. Now, the torque created by the weight of the boy is balanced by the torque created by the tension in the rope at point b. Since there is no other external torque acting on the system, the net torque is zero.
5. Therefore, the force on the rope can be calculated as the torque divided by the distance from the hinge to the rope attachment point. In this case, the distance is 2m.
6. The force (F) on the rope can be calculated using the formula: F = torque / distance. So, F = 200 Nm / 2m = 100 N.
Therefore, the force on the rope is 100 N.