A pole AB of length 10m and weighs 60ghas it's center of gravity 4m from the end A, and lies horizontally on the ground . Draw the diagram to illustrate the forces acting on the pole when the end B is lifted by a vertical force . Calculate the force required to begin to lift this end. Prove that the force applied at the end A qillnot be sufficient to lift the end A from the ground. Up
To draw the diagram illustrating the forces acting on the pole, you can follow these steps:
1. Draw a horizontal line to represent the ground.
2. On the left end of the ground line, mark point A.
3. From point A, draw a vertical line upward, representing the pole AB of length 10m.
4. On the right end of the pole, mark point B.
5. Draw an arrow pointing upward from point B to represent the vertical force lifting the end B of the pole.
Now, let's calculate the force required to begin lifting the end B of the pole. To do this, we need to consider the concept of torque (or moment).
The torque acting on an object is given by the formula:
Torque = Force × Perpendicular distance
In this case, the torque required to begin lifting the end B of the pole can be calculated as follows:
Torque = Force × Distance from the center of gravity to point B
Given that the center of gravity is 4m from point A and the total length of the pole is 10m, the distance from the center of gravity to point B is 10m - 4m = 6m.
To compute the force required to begin lifting the end B, we need to rearrange the above formula:
Force = Torque / Distance from the center of gravity to point B
Substituting the known values into the formula:
Force = 60g × 6m / 6m
= 60g
Therefore, the force required to begin lifting the end B is simply 60g, where g represents the acceleration due to gravity (approximately 9.8m/s²).
Now, let's prove that the force applied at the end A will not be sufficient to lift the end B from the ground. When a force is applied at point A to lift the pole, the torque generated can be calculated using the same formula as before:
Torque at A = Force × Distance from the center of gravity to point A
Substituting the known values into the formula:
Torque at A = 60g × 4m / 6m
= 40g
Since the torque needed to lift the end B is 60g, and the torque applied at point A is only 40g, it is clear that the force applied at the end A will not be sufficient to lift the end B from the ground.
This demonstrates that in order to lift the end B of the pole, a force equal to or greater than 60g is required.