Question

Тело массой 6 кг брошено вертикально вверх со скоростью 8 м/с. Тело поднимается на высоту 3 м, после чего начинает падать вниз. Считая, что тело теряет одинаковое количество энергии на преодоление сопротивления воздуха при движении вверх и вниз, определите импульс тела непосредственно перед падением на Землю. Ответ округлите до десятых. Ответ дайте в кг ⋅ м/с.

Answer 1

Ответ:

См фото

Объяснение:

Answer 2

Problem Analysis

We are given the following information: - Mass of the body, m = 6 kg - Initial velocity, v0 = 8 m/s - Height reached, h = 3 m

We need to determine the momentum of the body just before it hits the ground.

Solution

To solve this problem, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of a system remains constant if no external forces are acting on it.

The mechanical energy of the body at the highest point (when it reaches a height of 3 m) is equal to its initial mechanical energy. The mechanical energy of a body can be calculated using the formula:

E = KE + PE

Where: - E is the mechanical energy - KE is the kinetic energy - PE is the potential energy

At the highest point, the body has no kinetic energy because its velocity is zero. Therefore, the mechanical energy is equal to the potential energy:

E = PE

The potential energy of an object at a certain height is given by the formula:

PE = m * g * h

Where: - m is the mass of the body - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the height

Substituting the given values, we can calculate the potential energy at the highest point:

PE = 6 kg * 9.8 m/s^2 * 3 m = 176.4 J

Since the body loses an equal amount of energy due to air resistance during its upward and downward motion, the mechanical energy just before it hits the ground is also equal to 176.4 J.

The momentum of an object is given by the formula:

p = m * v

Where: - p is the momentum - m is the mass of the body - v is the velocity

To find the momentum just before the body hits the ground, we need to calculate the velocity. We can use the formula for kinetic energy to find the velocity:

KE = 0.5 * m * v^2

Rearranging the formula, we get:

v = sqrt(2 * KE / m)

Substituting the known values, we can calculate the velocity just before the body hits the ground:

v = sqrt(2 * 176.4 J / 6 kg) ≈ 8.16 m/s

Finally, we can calculate the momentum using the formula:

p = m * v = 6 kg * 8.16 m/s ≈ 48.96 kg·m/s

Therefore, the momentum of the body just before it hits the ground is approximately 48.96 kg·m/s.

Answer

The momentum of the body just before it hits the ground is approximately 48.96 kg·m/s.