A rope pulls a box along a floor with a force of 120 N at 25 degrees above the horizontal
Scalars & Vectors - OCR A-Level Physics
- A rope pulls a box along a floor with a force of 120 N at 25 degrees above the horizontal.
- Find the horizontal and vertical components of the pulling force.
$$\begin{aligned}
F_x &= F\cos\theta \\
&= 120 \times \cos(25^\circ) \\
&= 120 \times 0.906 \\
&= 108.8 \text{ N}
\end{aligned}$$
$$\begin{aligned}
F_y &= F\sin\theta \\
&= 120 \times \sin(25^\circ) \\
&= 120 \times 0.423 \\
&= 50.7 \text{ N}
\end{aligned}$$
- The horizontal component (108.8 N) pulls the box forward along the floor.
- The vertical component (50.7 N) acts upward, partially lifting the box and reducing the normal contact force.
- Check: sqrt(108.\(8^{2}\) + 50.\(7^{2}\)) = sqrt(11837 + 2570) = sqrt(14407) = 120 N. Correct.
Examiner Tips and Tricks
- Always verify your components using Pythagoras.
- If sqrt(F_\(x^{2}\) + F_\(y^{2}\)) does not equal the original force, you have made an error.