A uniform plank weighing 50N and 12m long is pivoted at a point of 4m from one end.A boy weighing 30N sits on a plank 7m from pivot.where must his elder brother whose weight is 80N sit to balance the plank horizontally
50/3 * 2 + 80*d = 2*50/3 * 4 + 30*7
d = 31/8 m
To balance the plank horizontally, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
Let's calculate the moments first. Moments are calculated by multiplying the weight of an object by its distance from the pivot point.
For the plank:
Weight of the plank = 50N
Distance of the plank from the pivot point = 4m
Moment of the plank = Weight of the plank × Distance of the plank
= 50N × 4m
= 200 Nm
For the boy:
Weight of the boy = 30N
Distance of the boy from the pivot point = 7m
Moment of the boy = Weight of the boy × Distance of the boy
= 30N × 7m
= 210 Nm
Now, we need to find the position where the elder brother, who weighs 80N, should sit to balance the plank horizontally.
Let's say the distance of the elder brother from the pivot point is "x" meters.
Moment of the elder brother = Weight of the elder brother × Distance of the elder brother
= 80N × x
According to the condition for balance:
Sum of clockwise moments = Sum of counterclockwise moments
(clockwise moments are negative, counterclockwise moments are positive)
-Hence, 200 Nm - 210 Nm + (80N × x) = 0
Simplifying the equation:
80N × x = 10 Nm - 200 Nm
80N × x = -190 Nm
x = -190 Nm / 80N
x = -2.375 m
Since the distance cannot be negative, we ignore the negative sign.
Therefore, the elder brother should sit approximately 2.375 meters from the pivot point in the opposite direction of the other person to balance the plank horizontally.