Discussion
A mass \(m\) = 10 kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s2 and that static and kinematic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is
Answer: A
Equilibrium is impossible for a spring force of 30 N.
The incline rises 3 m over 4 m, so \(\sin\theta = 0.6\) and \(\cos\theta = 0.8\). The spring pulls the mass up the slope. Along the incline:
\[ \begin{aligned} mg\sin\theta &= 100 \times 0.6 = 60\ \text{N (down the slope)} \\ \mu N &= 0.25 \times 100 \times 0.8 = 20\ \text{N} \end{aligned} \]
Friction can act either way, up to 20 N, so the spring force S must satisfy \(60 - 20 \le S \le 60 + 20\), that is \(40 \le S \le 80\) N. 45, 60 and 75 N all lie in this range; 30 N is too small to hold the mass even with full friction helping.
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