# Pulling a lawn roller is easier than to push it.

It is easier to pull a body than to push it. Suppose a force F is applied to pull a lawn roller of weight W. The force F has two rectangular components:

(i) Horizontal components F\;\cos\left(\theta\right) helps to move the roller forward.

(ii) Vertical component F\;\sin\left(\theta\right) acts in the upward direction.

If R is the normal reaction, then

R+F\;\sin\left(\theta\right)=W

[Equation the vertical components]

or, R=W-F\;\sin\left(\theta\right)

Force of kinetic friction,

f_k=\mu_k\;R=\mu_k\left(W-F\;\sin\left(\theta\right)\right)\;\;\;\;\;\;\;\;\;\;……….(1)

If a force F is applied to push a roller of weight W, then the normal reaction is

R'=W+F\;\sin\left(\theta\right)

Force of kinetic friction,

f'_k=\mu_k\;R'=\mu_k\left(W-F\;\sin\left(\theta\right)\right)\;\;\;\;\;\;\;\;\;\;……….(2)

Comparing (1) and (2), we find that f'_k>f_k

i.e., the force of friction is more in the case of a push than in the case of pull. So it is easier to pull a body than to push it.

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