небольшое тело массой м скользящее по m плоскости, наезжает на незакрепленную горку высотой h = 1,5 м и массой M =5m. при какой минимальной скорости v_0 тело сможет преодолеть горку. трением в системе пренебречь. ускорение свободного падения g=10м/с^2. ответ вырази в м/с и округли до целого значения.
To solve this problem, we need to use the principles of conservation of energy. Initially, the body has only kinetic energy due to its motion on the flat surface. As it approaches the hill, it starts gaining potential energy as it moves higher. The goal is to find the minimum initial velocity that will allow the body to have enough energy to overcome the hill.We will use the following equation: M*g*h + (1/2)*M*v_0^2 = (1/2)*M*v_final^2, where M is the total mass of the body, g is the acceleration due to gravity, h is the height of the hill and v_0 and v_final are the initial and final velocities respectively.
We can rearrange the equation to solve for v_0: v_0 = √(2*g*h). Plugging in the given values, we get v_0 = √(2*10*1.5) = 7.75 m/s. Therefore, the minimum initial velocity needed to overcome the hill is 7.75 m/s.
It is worth noting that in this solution, we have assumed the body to be a point mass and have neglected friction. In a real-life scenario, these factors would have an impact on the actual minimum velocity needed.
Happy sliding!
