Forces and Equilibrium: Question 6

Worked solution

Step 1: Identify the component required

The $60\text{ N}$ force acts at $35^\circ$ above the horizontal. To find its vertical component, we use the side of the right-angled triangle “opposite” the given angle, which corresponds to the sine ratio.

Step 2: Resolve the force

$F_{\text{vertical}} = 60\sin35^\circ$

Using $\sin35^\circ \approx 0.5736$: $F_{\text{vertical}} = 60 \times 0.5736\ldots \approx 34.4\text{ N}$

Why the other options are wrong

• B ($49.1\text{ N}$): this is $60\cos35^\circ$, using cosine instead of sine. This actually gives the horizontal component, not the vertical one.
• C ($60\text{ N}$): this uses the full force without resolving it, ignoring that only part of the $60\text{ N}$ acts vertically.
• D ($42.0\text{ N}$): this is $60\tan35^\circ$, applying the wrong trig ratio. The tangent ratio does not directly give either component of a force from its magnitude alone.

Final answer

• The vertical component is $\boxed{34.4}\text{ N}$, option A.