A vaulter holds a 26.90-N pole in equilibrium by exerting an upward force U with her leading hand and a downward force D with her trailing hand. Point C is the center of gravity of the pole, a=0.750 m, b=1.31 m, c=2.20 m. What is the magnitudes of U?

Check attachment for better understanding

Explanation:

Given that

a= 0.75m

b=1.31m

c= 2.2m

Weight of pole is 26.90

Then, Fg = Weight = 26.90

Using Equilibrium of forces

ΣFy = 0

U — D — Fg = 0

U — D = Fg

U — D = 26.9

To calculate U,

We will take moment about point A.

ΣMa = 0

Let the clockwise moment be positive and anti-clockwise be negative

Fg(a+b) — U(a) = 0

26.9(1.31+0.75) —0.75U = 0

26.9(2.06) = 0.75U

0.75U = 55.414

U = 55.414/0.75

U = 73.89 N

To calculate D,

U — D = 26.9

73.89—D =26.9

73.89—26.9 = D

D = 46.99N

Given Information:

Pole weight = w = 26.90 N

Force at point c = Fg

Force at point a = FD

distant between point a and b = 0.750 m

distant between point b and c = 1.31 m

Required Information:

Upward Force at point b = FU = ?  

Upward Force at point b = FU = 73.88 N

Explanation:

Please refer to the attached diagram,

Fg is the force due to gravity at point c acting downwards,

Fg = w = mg = 26.90 N

Let us take clockwise direction positive and anti-clockwise direction negative then applying the equilibrium condition of torque about point a yields,

ΣM = 0

FU(0.750) - Fg(0.750 + 1.31) = 0

0.750FU - 2.06Fg = 0

0.750FU = 2.06Fg

FU = 2.06Fg/0.750

FU = 2.06(26.90)/0.750

FU = 73.88 N

Bonus:

The other force FD can now be found. Let upward direction of force is positive and downward direction of force is negative.

The the sum of forces acting in the y-axis is given by

ΣFy = 0

-FD + FU - Fg = 0

Where FD is the force at point a acting downwards, FU is the force at point b acting upwards, and Fg is the force due to gravity at point c acting downwards.

-FD + FU - 26.90 = 0

FD = FU - 26.90

FD = 73.88 - 26.90

FD = 46.98 N

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force