<p>In a physics experiment, a formula is given by \(F = mg \sin(\theta) - \mu mg \cos(\theta)\), where&nbsp;\(\mu\), \(g\) are constants and \(m\), \(\theta\) may vary. It is given that&nbsp;\(g = 9.8\), \(\mu = 0.5\), \(m &gt; 0\) and \(0 &lt; \theta &lt; 90{}^\circ\).</p>
<ol class="i-list"><li><div class="list-item-paragraph">Evaluate \(F\) given that&nbsp;\(m = 15\) and \(\theta = 30{}^\circ\).<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the value of \(\theta\) such that&nbsp;\(F = 0\). Note that&nbsp;\(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Another variable, \(a\), is defined by \(a = \frac{F}{m}\). Express \(a\) in terms of \(\mu\), \(g\) and \(\theta\).</div><div class="list-item-paragraph">Hence find the range of values of \(\theta\) such that&nbsp;\(a &gt; 0\).</div><div class="list-item-paragraph">You may assume the fact that&nbsp;\(\tan(\theta) &gt; p \iff \theta &gt; \tan^{-1}(p)\) for&nbsp;\(0 &lt; \theta &lt; 90{}^\circ\).<span class="inline-marks">[2]</span></div></li></ol>

In a physics experiment, a formula is given by \(F = mg \sin(\theta) - \mu mg \cos(\theta)\), where \(\mu\), \(g\) are constants and \(m\), \(\theta\) may vary. It is given that \(g = 9.8\), \(\mu = 0.5\), \(m > 0\) and \(0 < \theta < 90{}^\circ\).

Evaluate \(F\) given that \(m = 15\) and \(\theta = 30{}^\circ\).

Find the value of \(\theta\) such that \(F = 0\). Note that \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).

Another variable, \(a\), is defined by \(a = \frac{F}{m}\). Express \(a\) in terms of \(\mu\), \(g\) and \(\theta\).

Hence find the range of values of \(\theta\) such that \(a > 0\).

You may assume the fact that \(\tan(\theta) > p \iff \theta > \tan^{-1}(p)\) for \(0 < \theta < 90{}^\circ\).

IP2 Class Test (May 2025) Q6

IP2 Class Test (May 2025) Q6

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