A uniform plank weighing 50N and 12m long is pivoted at a point of 4m from one end.A boy weighing 30N sits on the plank 7m from pivot.Where must his elder brother whose weight is 80N sit to balance the plank horizontally
5.00
A uniform plann weighing 50newton and 13meter long is pivoted at a point 4 meter from one end A boy weighing 30newton sit on a plank7 meter from the pivot where must his elder brother whose weight is 80newton sit to balance the plank horizontally
Not correct
To find the position where the elder brother must sit to balance the plank horizontally, we need to consider the torques acting on the plank.
Torque is the product of the force applied and the perpendicular distance from the pivot point. For the plank to be balanced horizontally, the sum of the clockwise torques must be equal to the sum of the counterclockwise torques.
First, let's calculate the torque caused by the weight of the uniform plank. The weight of the plank is acting vertically downward at its center, which is at a distance of 6m from the pivot (half of the plank's length). The torque from the plank's weight is:
Torque_plank = weight_plank * distance_plank = 50N * 6m = 300Nm (clockwise)
Next, let's calculate the torque caused by the boy sitting on the plank. The boy's weight is acting vertically downward at a distance of 7m from the pivot. The torque from the boy's weight is:
Torque_boy = weight_boy * distance_boy = 30N * 7m = 210Nm (clockwise)
Now, we need to find the position where the elder brother must sit (let's call this distance x). The elder brother's weight is acting vertically downward at a distance of (4m + x) from the pivot. The torque from the elder brother's weight is:
Torque_brother = weight_brother * distance_brother = 80N * (4m + x)
For the plank to be balanced horizontally, the sum of the clockwise torques (300Nm + 210Nm) must be equal to the sum of the counterclockwise torque (Torque_brother).
300Nm + 210Nm = 80N * (4m + x)
510Nm = 320N * (4m + x)
Divide both sides of the equation by 320N:
1.59375m = 4m + x
Rearrange the equation to isolate x:
x = 1.59375m - 4m
x = -2.40625m
Since distance cannot be negative, it means that the elder brother needs to sit 2.40625m to the left (in the counterclockwise direction) from the pivot point to balance the plank horizontally.
Draw a free body diagram and set the total moment about the fulcrum/pivot equal to zero. Let x be the distance of the elder brother from the pivot.
80*x = 50*2 + 30*7 = 310 N*m
x = 3.87 m (on the opposite side of the pivot from the 30 N brother)
This location is quite near the edge of the plank