a bench is 2.4m long.the legs are attached .3m from each end.if 3 boys weighing 500n,750n,1000n seated.4,1.2m,2m from end of the bench,what force must eachset of leg exert

To find the force that each set of legs must exert in order to support the boys on the bench, we can use the principle of equilibrium. According to this principle, the sum of all the forces acting on an object in equilibrium is equal to zero.

Let's calculate the total weight of the boys seated on the bench. The weight of an object can be calculated using the equation:

Weight = mass x gravity

Since weight is the force that pulls an object towards the center of the Earth, we can assume a standard gravity value of 9.8 m/s^2.

For the first boy weighing 500 N, his weight would be:

Weight_1 = 500 N

For the second boy weighing 750 N:

Weight_2 = 750 N

And for the third boy weighing 1000 N:

Weight_3 = 1000 N

Now, let's determine the distances of each boy from one end of the bench:

For the first boy seated 4 m from one end:

Distance_1 = 4 m

For the second boy seated 1.2 m from the same end:

Distance_2 = 1.2 m

And for the third boy seated 2 m from the same end:

Distance_3 = 2 m

To calculate the force each set of legs must exert, we need to consider the moments caused by the weights of the boys. The moment of force (torque) is calculated by multiplying the force by the perpendicular distance from the point of rotation. In this case, the point of rotation is the set of legs.

For equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments. Mathematically, it can be represented as:

Sum of clockwise moments = Sum of anticlockwise moments

Now, let's calculate the moments caused by the weights:

Clockwise moments:

Moment_1 = Weight_1 * Distance_1
Moment_2 = Weight_2 * Distance_2
Moment_3 = Weight_3 * Distance_3

Anticlockwise moments:

Moment_4 = Weight_4 * Distance_4
Moment_5 = Weight_5 * Distance_5
Moment_6 = Weight_6 * Distance_6

Since the bench is symmetrical and the legs are attached at equal distances from each end, the moments caused by the 4th, 5th, and 6th boys will be the same as the 1st, 2nd, and 3rd boys, respectively.

Now let's put all the moments into the equation:

Moment_1 + Moment_2 + Moment_3 = Moment_4 + Moment_5 + Moment_6

Since the distances of the legs from each end are given as 0.3 m, we can substitute them into the equation:

Weight_1 * Distance_1 + Weight_2 * Distance_2 + Weight_3 * Distance_3 =
Weight_4 * 0.3 + Weight_5 * 0.3 + Weight_6 * 0.3

From this equation, we can solve for the unknown force Weight_4, Weight_5, and Weight_6.