Question

Determine the magnitude of frictional force in each of the following cases:

• A. 20 N, 50 N,0 N
• B. 50 N, 100 N, 103 N
• C. 20 N, 0 N, 50 N
• D. 20 N, 0 N, 10 N

Answer 1

The correct option is A

20 N, 50 N,0 N

(FBD for case (a)) $N=100N\to f_{max}=\mu N=0.2\times 100=20NAnd,mg=(5\times 10)=50N\therefore mg>f_{max}\therefore f=20N$



(FBD for case (b))
$N=500N\to f_{max}=\mu N=0.2\times 600=100NAnd,mg=50N\therefore mg<f_{max}\therefore f=50N$

(FBD for case (c))
$N=100cos30\circ =86.6N\therefore f_{max}=\mu N=0.2\times 86.6N=17.32NNow,f+100sin30\circ =mg\Rightarrow f=mg-100sin30\circ =50-50=0N\therefore f<f_{max}\therefore f=0N$
So, f = 0 N and it is less than the limiting value.