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<h2>Example: Newton's Second Law: Man Pulling a Box</h2>
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<h3>Question</h3>
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<p>A man is pulling a $\text{20}$ $\text{kg}$ box with a rope that makes an angle of $\text{60}$$\text{°}$ with the horizontal. If he applies a force of magnitude $\text{150}$ $\text{N}$ and a frictional force of magnitude $\text{15}$ $\text{N}$ is present, calculate the acceleration of the box.</p>
<img alt="868fc4de1803d87e56e96b3d71a3c3e4.png" src="https://data.ulearngo.com/assets/b9034ae9-6e6d-4482-b9aa-52c5759da4a8"/></div>
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<h3>Step 1: Draw a force diagram or free body diagram</h3>
<p>The motion is horizontal and therefore we will only consider the forces in a horizontal direction. Remember that vertical forces do not influence horizontal motion and vice versa.</p>
<img alt="00739e603136597df0b4b687526465a6.png" src="https://data.ulearngo.com/assets/6bf57b0f-64f7-4cce-8092-3d3f53a44263"/></div>
<p><img alt="965663764d93eb6ce9b95357e3dafa5f.png" src="https://data.ulearngo.com/assets/48cd96c4-7b91-4a6c-9d4e-b1d3578d34b1"/></p>
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<h3>Step 2: Calculate the horizontal component of the applied force</h3>
<p>We first need to choose a direction to be the positive direction in this problem. We choose the positive $x$-direction (to the right) to be positive.</p>
<p>The applied force is acting at an angle of $\text{60}$$\text{°}$ to the horizontal. We can only consider forces that are parallel to the motion. The horizontal component of the applied force needs to be calculated before we can continue: \begin{align*} F_x &amp; = F_{applied}\cos(\theta) \\ &amp;= \text{150}\cos(\text{60}\text{°}) \\ &amp; = \text{75}\text{ N} \end{align*}</p>
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<h3>Step 3: Calculate the acceleration</h3>
<p>To find the acceleration we apply Newton's second law: \begin{align*} F_R&amp;=ma \\ F_x+F_f&amp;=(\text{20})a \\ (\text{75}) + (-\text{15})&amp;= (\text{20})a\\ a &amp; = \frac{\text{60}}{\text{20}} \\ a &amp; = \text{3}\text{ m·s$^{-2}$} \end{align*}The acceleration is $\text{3}$ $\text{m·s$^{-2}$}$ to the right.</p>
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Man Pulling a Box Example

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

Physics

Learn about the principles of motion and forces, including static and kinetic friction, normal forces, tension, and Newton&#8217;s laws, with practical examples such as lifting weights, rockets, and balloons.


Man Pulling a Box Example

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