Question

Пуля, массой 10 г, летящая горизонтально со скоростью 300 м/с, ударяет в подвешенный на нитях деревянный брусок массой 6 кг и застревает в нем. Определите на какую высоту поднимается брусок.

Answer 1

Ответ:

1) Определим скорость бруска после попадания пули: V = mп * Vп / (mп + mб) = 0,01 * 300 / (0,01 + 6) = 0,5 м/с. 2) Вычислим высоту подъема бруска: (mп + mб) * V 2 / 2 = (mп + mб) * g * h, откуда h = V 2 / (2 * g) = 0,5 2 / (2 * 10) = 0,0125 м (12,5 мм). Ответ: Брусок поднимется на высоту 12,5 мм.

Answer 2

Calculation of the Height

To determine the height to which the wooden block is raised when a bullet with a mass of 10 g and a horizontal velocity of 300 m/s strikes and becomes embedded in it, we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on the system.

In this case, the momentum of the bullet before the collision is equal to the momentum of the bullet and the wooden block after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity.

Let's denote the mass of the bullet as m1 (10 g = 0.01 kg) and the mass of the wooden block as m2 (6 kg). The initial velocity of the bullet is v1 (300 m/s).

The momentum before the collision is given by:

p1 = m1 * v1

The momentum after the collision is given by:

p2 = (m1 + m2) * v2

Since the bullet becomes embedded in the wooden block, their final velocity after the collision is the same. Let's denote this final velocity as v2.

According to the principle of conservation of momentum, we have:

p1 = p2

Substituting the expressions for p1 and p2, we get:

m1 * v1 = (m1 + m2) * v2

Solving for v2, we find:

v2 = (m1 * v1) / (m1 + m2)

Now, we can use the equation for the height gained by an object in free fall to calculate the height to which the wooden block is raised.

The equation for the height gained is given by:

h = (v2^2) / (2 * g)

Where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the value of v2 into the equation, we get:

h = ((m1 * v1) / (m1 + m2))^2 / (2 * g)

Let's calculate the height using the given values:

m1 = 0.01 kg v1 = 300 m/s m2 = 6 kg g = 9.8 m/s^2

Substituting these values into the equation, we find:

h = ((0.01 * 300) / (0.01 + 6))^2 / (2 * 9.8)

Calculating this expression, we find that the height to which the wooden block is raised is approximately 0.045 meters.

Please note that this calculation assumes ideal conditions and neglects factors such as air resistance and the elasticity of the collision.