A pole AB of Length 10.0m and weight 600N has its centre of gravity 4.0m from the end A, and lies on horizontal ground. Draw a diagram to show the forces acting on the pole when end B is lifted by a vertical force. Calculate the force required to being lift this end. Prove that this force applied at the end A will not be sufficient to lift the end A from the ground
In order to draw a diagram showing the forces acting on the pole, we need to consider two main forces: the weight of the pole and the force lifting end B.
First, let's draw a horizontal line to represent the ground. Mark a point A on the left side of the line, representing the end of the pole that remains on the ground. Then, mark a point B on the right side of the line, representing the end of the pole that is being lifted.
Next, draw a vertical line from point A to represent the weight of the pole. Label this line as F weight, which is equal to 600N. This force acts downward, towards the ground.
Now, draw a diagonal line from point B towards point A to represent the force lifting end B. Label this line as F lift, representing the force required to lift end B. This force acts upward, away from the ground.
Finally, draw a horizontal line from point A to represent the force required to balance the weight of the pole. Label this line as F balance, which is the force applied at the end A in order to lift the end B. This force acts to the right, counteracting the weight of the pole.
To calculate the force required to lift end B, we can use the concept of torque. Torque is the mathematical representation of the ability of a force to rotate an object. The torque produced by the weight of the pole is equal to the weight (F weight) multiplied by the distance from the center of gravity to the point of rotation (4.0m).
Torque(weight) = F weight * distance from center of gravity = 600N * 4.0m = 2400 N·m
To balance the torque produced by the weight, the force applied at the end A (F balance) must create an equal and opposite torque. In order for these torques to be equal, the force applied at the end A must be greater than F lift. Therefore, the force applied at the end A will not be sufficient to lift end A from the ground.