(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Sam is pulling a box of mass 30kg on a horizontal floor with a force F_{T}= <50N, 30N>. The frictional force acting on the box by the floor is 20N.

A) By using Newton's second law find the acceleration of the block.

B) What is the normal force acting on the block by the floor?

C) What is the coefficient of kinetic friction between the floor and the box?

2. Relevant equations

F_{net}=F_{x}+F_{y}

F=ma

F_{normal}=m(g+a_{y}) (g is approximated gravity coefficient, 9.8m/s^{2})

μ_{k}F_{normal}=F_{k}(force of kinetic friction)

|F|=√F_{y}^{2}+F_{x}^{2}

3. The attempt at a solution

A)

F_{TX}=50N - 20N = 30N

F_{TY}=30N +294N = 324N

|F|=√(324N)^{2}+ (30N)^{2}= 326.77N

F=ma

326.77N = (30kg)a

a = 10.89 m/s^{2}

B)

F_{normal}=m(g+a_{y})

F_{normal}=(30kg)(9.8m/s^{2}+10.89 m/s^{2})

= 620.7N

C)

μ_{k}F_{normal}=F_{k}

μ_{k}(620.7N) = 20N

μ_{k}= .0322

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# Homework Help: Box being pulled across horizontal floor with friction

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