Mechanical 43721

A body weighing 2 kg falls from a height of 45 m in a free fall. What will be its potential energy and total mechanical energy after 2 s from the beginning of the movement?

Correct answer:

E =  497.9556 J
E₂ =  882.9 J

Step-by-step explanation:

$$\begin{gathered} m=2\text{kg} \\ h=45\text{m} \\ t=2\text{s} \\ g=9.81{\text{m/s}}^2 \\ s=\frac{1}{2}\cdot g\cdot t^2=\frac{1}{2}\cdot 9.81\cdot 2^2=\frac{981}{50}=19.62\text{m} \\ {h}_2=h-s=45-\frac{981}{50}=\frac{45\cdot 50}{50}-\frac{981}{50}=\frac{2250}{50}-\frac{981}{50}=\frac{2250-981}{50}=\frac{1269}{50}=25.38\text{m} \\ E=m\cdot g\cdot h_2=2\cdot 9.81\cdot 25.38=497.9556\text{J} \end{gathered}$$

$$\begin{gathered} v=g\cdot t=9.81\cdot 2=\frac{981}{50}=19.62\text{m/s} \\ K=\frac{1}{2}\cdot m\cdot v^2=\frac{1}{2}\cdot 2\cdot {\frac{981}{50}}^2=384.9444\text{J} \\ {E}_2=E+K=497.9556+384.9444=\frac{8829}{10}\text{J}=882.9\text{J} \end{gathered}$$

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