a uniform pole 7m long and weighing 10kg suppoted by a boy 2m from one end man3 from other end

and the question is?

Solution to the question

To find the force exerted by the boy and the man in supporting the pole, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point when the object is in equilibrium.

In this case, the pole is in equilibrium, so we can use the principle of moments to calculate the forces exerted by the boy and the man.

Let's assume that the weight of the pole is acting at its center, which is at a distance of 7/2 = 3.5m from either end.

The boy is supporting the pole 2m from one end, so the force exerted by the boy can be represented as Fboy × 2m, and its clockwise moment is given by Fboy × 2m.

Similarly, the man is supporting the pole 3m from the other end, so the force exerted by the man can be represented as Fman × 3m, and its anticlockwise moment is given by Fman × 3m.

Since the pole is in equilibrium, we can set up the equation using the principle of moments:

Fboy × 2m = Fman × 3m

We also know that the weight of the pole, which is acting at its center, is given by the formula:

Weight = mass × gravitational field strength

The mass of the pole is given as 10kg, and the gravitational field strength can be assumed to be 9.8 m/s².

Weight = 10kg × 9.8 m/s² = 98N

Since the weight is acting at the center of the pole, and we assumed the center to be at 3.5m from either end, the clockwise moment is given by:

Clockwise moment = Weight × 3.5m = 98N × 3.5m = 343N·m

Now, we can substitute the clockwise moment into the equation:

343N·m = Fman × 3m

Simplifying the equation, we can solve for Fman:

Fman = 343N·m / 3m = 114.33N

So, the force exerted by the man in supporting the pole is approximately 114.33 Newtons.

To find the force exerted by the boy, we can substitute this value of Fman back into the equation:

Fboy × 2m = 114.33N × 3m

Simplifying the equation, we can solve for Fboy:

Fboy = (114.33N × 3m) / 2m = 171.5N

So, the force exerted by the boy in supporting the pole is approximately 171.5 Newtons.

Therefore, the boy exerts a force of approximately 171.5 Newtons and the man exerts a force of approximately 114.33 Newtons in supporting the pole.