Question

Пружину жесткостью 40Н/м сжали на 10 см. Какую скорость приобретет пуля массой 25г при выстреле в горизонтальном направлении?

Answer 1

Calculation of the Bullet's Velocity

To calculate the velocity acquired by the bullet when compressed by a spring with a stiffness of 40 N/m and compressed by 10 cm, we can use the principle of conservation of mechanical energy.

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

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

Where: - k is the stiffness of the spring (40 N/m) - x is the compression distance (10 cm = 0.1 m)

Substituting the given values into the formula, we get:

PE = (1/2) * 40 N/m * (0.1 m)^2

Simplifying the equation, we find:

PE = 0.2 J

The potential energy stored in the spring is equal to the kinetic energy acquired by the bullet when it is released. The kinetic energy can be calculated using the formula:

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

Where: - m is the mass of the bullet (25 g = 0.025 kg) - v is the velocity of the bullet

We can equate the potential energy to the kinetic energy:

PE = KE

0.2 J = (1/2) * 0.025 kg * v^2

Simplifying the equation, we find:

v^2 = (0.2 J * 2) / 0.025 kg

v^2 = 16 m^2/s^2

Taking the square root of both sides, we find:

v = 4 m/s

Therefore, the bullet will acquire a velocity of 4 m/s when fired horizontally.