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In Fig. \( 6-29 \), a force \( \vec{P} \) acts on a block weighing \( 45 \mathrm{~N} \). The block is initially at rest on a plane inclined at angle \( \theta=15^{\circ} \) to the Figure 6-39 horizontal. The positive direction of the \( x \) axis is up the plane. Between block and plane, the coefficient of static friction is \( \mu_{\mathrm{s}}=0.50 \) and the coefficient of kinetic friction is \( \mu_{k}=0.34 \). In unitvector notation, what is the frictional force on the block from the plane when \( \vec{P} \) is (a) \( (-5.0 \mathrm{~N}) \hat{\mathrm{i}} \), (b) \( (-8.0 \mathrm{~N}) \hat{\mathrm{i}} \), and (c) \( (-15 \mathrm{~N}) \hat{\mathrm{i}} \) ?
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