Kevin S. Huang

2009: Problem 15

Topic: Dynamics
Concepts: Forces in mechanics, Newton’s laws

Solution:

Since the suitcase is moving at constant velocity, the net force on the suitcase is zero. By Newton’s 2nd law, we have

F\cos\theta=f

in the horizontal direction and

F\sin\theta+N=mg

in the vertical direction. Since $f=\mu N$ , we substitute in the first and second equations:

\mu=\frac{F\cos\theta}{N}=\frac{F\cos\theta}{mg-F\sin\theta}=\frac{(100\,\mathrm{N})(\cos 30^{\circ})}{(22\,\mathrm{kg})(10\,\mathrm{m/s^2})-(100\,\mathrm{N})(\sin 30^{\circ})}=0.509

so the answer is C.