Question

ОЧЕНЬ СРОЧНО!!!! Для выстрела пружину игрушечного пистолета с жёсткость 10kH/m стали на 4 см. Какую скорость при выстрела приобрела дробинка массой 10 г, если выстрел произведён в горизонтальном направлении? На какую высоту сможет подняться дробинка, если выстрел произвести в вертикальном направлении?

Answer 1

Закон сохранения энергии: m * V2 / 2 = k * Δx2 / 2, откуда V = √(k * Δx2 / m

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Answer 2

Calculation of Projectile Velocity:

To calculate the velocity of the projectile, we can use the principle of conservation of mechanical energy. The potential energy stored in the spring is converted into kinetic energy of the projectile.

The potential energy stored in the spring is given by the formula:

Potential Energy (PE) = (1/2) * k * x^2

Where: - k is the spring constant (stiffness) of the spring, given as 10 kH/m (kiloHertz per meter). - x is the displacement of the spring, given as 4 cm (0.04 m).

The kinetic energy of the projectile is given by the formula:

Kinetic Energy (KE) = (1/2) * m * v^2

Where: - m is the mass of the projectile, given as 10 g (0.01 kg). - v is the velocity of the projectile.

According to the principle of conservation of mechanical energy, the potential energy stored in the spring is equal to the kinetic energy of the projectile:

PE = KE

Substituting the formulas for potential energy and kinetic energy, we can solve for the velocity of the projectile:

(1/2) * k * x^2 = (1/2) * m * v^2

Simplifying the equation:

k * x^2 = m * v^2

Solving for v:

v = sqrt((k * x^2) / m)

Now we can substitute the given values into the equation to find the velocity of the projectile.

Calculation of Projectile Velocity:

Substituting the given values into the equation:

v = sqrt((10 kH/m * (0.04 m)^2) / 0.01 kg)

Calculating the value:

v ≈ 2.828 m/s

Therefore, the velocity of the projectile is approximately 2.828 m/s when fired in the horizontal direction.

Calculation of Projectile Height:

To calculate the height the projectile can reach when fired vertically, we can use the equations of motion.

The initial velocity of the projectile when fired vertically is the same as the velocity calculated earlier, which is approximately 2.828 m/s.

The height the projectile can reach can be calculated using the formula:

Height (h) = (v^2) / (2 * g)

Where: - v is the initial velocity of the projectile. - g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

Substituting the given values into the equation:

h = (2.828 m/s)^2 / (2 * 9.8 m/s^2)

Calculating the value:

h ≈ 0.408 m

Therefore, the projectile can reach a height of approximately 0.408 m when fired vertically.

Please note that these calculations assume ideal conditions and do not take into account factors such as air resistance.