New solution

Valter edited
revision #20009 newer →
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+### Statement
+
+$2.3.13.$ [Insert the problem statement]
+
+### Solution
+
+### Statement
+
+$2.3.13.$ A load of mass $m$ is slowly pulled up to a height $h$ along an inclined plane using a block and a cable. The work done during this process is $A$. Then the cable is released, and the load slides down. What velocity will it gain by the time it reaches the starting point?
+
+![For problem $2.3.13$|446x249, 40%](../../img/2.3.13/2.3.13.png)
+
+### Solution
+
+The difference between the work of the pulling force and the work of friction is equal to the change in potential energy:
+$$
+A - A_{\\text{f}} = mgh
+$$
+During the slide down from the top, friction performs the same amount of work. Let us write the law of conservation of energy:
+$$
+A_{\\text{f}} + \\frac{mv^2}{2} = mgh
+$$
+Substitute the work of friction to express the kinetic energy:
+$$
+\\frac{mv^2}{2} = 2mgh - A
+$$
+From this, we find the velocity the load will gain upon reaching the starting point:
+$$
+v = \\sqrt{4gh - 2A/m}
+$$
+
+#### Answer
+$v = \\sqrt{4gh - 2A/m}$
+
+#### Answer
+
+[Insert a concise answer or boxed result]