Question

Баскетбольный мяч массой т = 600 г падает с нулевой начальной скоростью с высоты Н 10 м. При ударе о горизонтальную поверхность земли потери механической энергии составляют Q 12 Дж. Определи максимальную высоту h, на которую поднимется мяч после удара. Сопротивлением воздуха можно пренебречь.​

Answer 1

Ответ:

mgH– Q = mv2/2

Отсюда находите v2

v2 = 2(mgH– Q)/m = 2(0.6·10·10–12)/0.6 = 160

Высота подъема будет

h = v2/2g = 160/20 = 8 м

Ответ: 8

Answer 2

Problem Analysis

We are given the mass of a basketball, the initial height from which it is dropped, and the mechanical energy loss upon impact with the ground. We need to determine the maximum height the ball will reach after the impact.

Solution

To solve this problem, we can use the principle of conservation of mechanical energy. The mechanical energy of the ball at the initial height is equal to the mechanical energy of the ball at the maximum height.

The mechanical energy of an object is the sum of its kinetic energy and potential energy. In this case, the ball is dropped from rest, so its initial kinetic energy is zero. Therefore, the mechanical energy at the initial height is equal to the potential energy of the ball.

The potential energy of an object at a certain height is given by the formula: potential energy = mass * gravity * height, where mass is the mass of the object, gravity is the acceleration due to gravity, and height is the height above the reference point.

After the ball impacts the ground, some mechanical energy is lost due to various factors such as deformation and heat. The mechanical energy loss is given as Q = 12 J.

Using the principle of conservation of mechanical energy, we can equate the mechanical energy at the initial height to the mechanical energy at the maximum height:

potential energy at initial height - mechanical energy loss = potential energy at maximum height

Let's calculate the maximum height using the given values.

Calculation

Given: - Mass of the basketball (m) = 600 g = 0.6 kg - Initial height (h) = 10 m - Mechanical energy loss (Q) = 12 J - Acceleration due to gravity (g) = 9.8 m/s^2

Using the formula for potential energy, we can calculate the potential energy at the initial height:

potential energy at initial height = mass * gravity * height

Substituting the given values:

potential energy at initial height = 0.6 kg * 9.8 m/s^2 * 10 m = 58.8 J

Now, we can use the principle of conservation of mechanical energy to find the maximum height:

potential energy at maximum height = potential energy at initial height - mechanical energy loss

potential energy at maximum height = 58.8 J - 12 J = 46.8 J

To find the maximum height, we can rearrange the formula for potential energy:

potential energy at maximum height = mass * gravity * maximum height

Rearranging the formula:

maximum height = potential energy at maximum height / (mass * gravity)

Substituting the values:

maximum height = 46.8 J / (0.6 kg * 9.8 m/s^2) ≈ 7.83 m

Therefore, the maximum height the basketball will reach after the impact is approximately 7.83 meters.

Answer

The maximum height the basketball will reach after the impact is approximately 7.83 meters.