Question

A man pulls on a cord attached to heavy $200N$ block. The coefficient of static friction between the box and the floor is $\mu =0.5$.
If the cord makes an angle of $\theta ={30.0}^o$ with the floor, what normal force $F_N$ will the floor be exerting on the block when the man is exerting enough force so that the box is barely about to move?

• A. $78N$
• B. $100N$
• C. $142N$
• D. $155N$
• E. $189N$

Answer 1

Answer: (D)

$155N$

Balancing force in vertical direction,

$Tsin\theta +N=W$

Balancing forces in horizontal direction,

$Tcos\theta =\mu N$

Solving the equations gives,

$(\mu tan\theta +1)N=W$

$⟹N=\frac{W}{\mu tan\theta +1}$

$=\frac{200}{\frac{0.5}{\sqrt{3}}+1}$

$=155N$