You're carrying a 3.2-m-long, 24kg pole to a construction site when you decide to stop for a rest. You place one end of the pole on a fence post and hold the other end of the pole 35cm from its tip.

How much force must you exert to keep the pole motionless in a horizontal position? N

Express your answer using two significant figures

Answer

given,

length of the pole = 3.2 m

mass of the pole = 24 Kg

Let the tension in fence post = T₁

let the tension in your hand = T₂

equating the vertical forces

T₁ + T₂ = mg

T₁ + T₂ = 24 x 9.8 ... (1)

now,

equation of moment with center

T₁ (1.6 m) = T₂ (1.25 m) ... (2) (∵ 1.6 m - 0.35 m = 1.25 m)

T₂ = 1.28 T₁

from equation (1)

T₁ + 1.28 T₁ = 235.2

2.28 T₁ = 235.2

T₁ = 103.16 N

now,

T₂ = 1.28 x 103.16

T₂ = 132.045 N

force exerted to keep the pole motion less is equal to T₁ = 103.16 N, T₂ = 132.045 N