Question

При подготовке пружинного пистолета к выстрелу пружину с жесткостью 1000H/м сжали на 3 см. Какую скорость приобретает снаряд массой 45 г при выстреле в горизонтальном направлении. Пожалуйста помогите, даю 50 баллов​

Answer 1

Из закона сохранения энергии : Потенциальная энергия пружины перейдет в кинетическую энергию снаряда .

Kx^2 /2 = mv^2/2

V =✓kx^2/m

V ✓ 1000 * 0,0009 / 0,045 = ✓20≈

4,5м/с

Answer 2

Calculation of Projectile Speed

To calculate the speed of the projectile, we can use the principle of conservation of mechanical energy. When the spring is compressed, it stores potential energy, which is then converted into kinetic energy of the projectile when released.

The potential energy stored in the spring can be calculated using the formula:

Potential Energy (PE) = 0.5 * k * x^2

Where: - k = spring constant (stiffness) = 1000 N/m - x = compression of the spring = 0.03 m (3 cm)

The potential energy stored in the spring can be calculated as follows: PE = 0.5 * 1000 * (0.03)^2 = 0.45 J

This potential energy will be converted into the kinetic energy of the projectile. The kinetic energy of the projectile can be calculated using the formula:

Kinetic Energy (KE) = 0.5 * m * v^2

Where: - m = mass of the projectile = 0.045 kg (45 g) - v = velocity of the projectile (what we want to find)

Equating the potential energy to the kinetic energy, we get: 0.45 = 0.5 * 0.045 * v^2

Solving for v, we get: v = sqrt(2 * 0.45 / 0.045) = 6 m/s

Therefore, the speed of the projectile when fired horizontally is 6 m/s.