A uniform pole 7m long and weighing 10kg is supported by a boy 2m from one end and a man 3m from the other end.At what point must a 20kg weight be attached so that the man would support thrice as much weight as the boy?
from left end where x = 0
b up at x = 2.0
10 down at x = 3.5
m up at x = 4.0
20 down at x = x
and
m = 3 b
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forces up = forces down
b + m = 10 + 20 = 30
moments clockwise = moments counterclockwise about x = 0
10*3.5 + 20 x = b * 2 + m *4
so
20 x = 2 b + 4 m -35
b + m = 30
m = 3 b
-----------------------------
b + 3 b = 30
b = 30/4 = 15/2 = 7.5
m = 3 b = 22.5
then
20 x = 2 b + 4 m -35
20 x = 15 + 90 - 35 = 70
x = 7/2 = 3.5
LOL right at the middle
check
now we have 22.5+ 10 = 32.5 down at the middle
b*distance to middle = 22.5 * m's distance to middle ?
7.5 * (3.5-2) = 22.5 * (4.0 - 3.5)?
7.5 * 1.5 = 22.5 * .5 ?
YES ! Caramba :)
(should have seen it right from the start though)
thanks but is this answer correct
0.1
a uniform pole 7m long weighing 10kg is supported by a boy 2m from one end and a man 3m from the other end. at what point must a 20kg weight be attached so that man would support thrice as much weight as the boy
I want answer I’m confused here
How did u solve it
Am confused as well how come of 2.0, 4.0 , 3 .5 . Am not happy with this solving
This does not make muçh sense
To solve this problem, we can use the principle of moments or torque. The torque is given by the product of the force applied to an object and the perpendicular distance from the point of rotation (fulcrum).
Let's first calculate the total torque exerted by the boy and the man on the pole. The torque exerted by the boy can be calculated as follows:
Torque_by_boy = (force_by_boy) * (distance_from_fulcrum_to_boy)
= (force_by_boy) * (2m)
Similarly, the torque exerted by the man can be calculated as follows:
Torque_by_man = (force_by_man) * (distance_from_fulcrum_to_man)
= (force_by_man) * (3m)
According to the problem, the man must support thrice as much weight as the boy. Therefore, we can express the relationship between the forces as:
force_by_man = 3 * force_by_boy
Now, let's determine the torque exerted by the weight attached to the pole. We can denote the force exerted by the weight as force_by_weight. The torque exerted by the weight can be calculated as:
Torque_by_weight = (force_by_weight) * (distance_from_fulcrum_to_weight)
Since the weight must balance the torque exerted by the boy and the man, the total torque on the pole must be zero. Therefore, we can set up the equation:
(Torque_by_boy) + (Torque_by_man) + (Torque_by_weight) = 0
Substituting the torque equations and the relationship between the forces, we get:
(force_by_boy * 2m) + (3 * force_by_boy * 3m) + (force_by_weight * distance_from_fulcrum_to_weight) = 0
Now, let's substitute the given values into the equation. The pole's weight is 10kg, so the force exerted by the boy is 10 * 9.8 N (using the acceleration due to gravity, g = 9.8 m/s²). The distance from the fulcrum to the weight is unknown and represented by x:
(10 * 9.8 N * 2m) + (3 * (10 * 9.8 N) * 3m) + (20kg * 9.8 N * x) = 0
Now, you can solve this equation to find the value of x, which represents the distance from the fulcrum to where the 20kg weight should be attached on the pole.