Question

Пуля массой 10 г, летящая горизонтально, пробивает деревянный брусок массой 200 г, подвешенный на длинной нити. При этом скорость пули изменяется от 100 м/с до 50 м/с. Пренебрегая смещением бруска во время удара, определите, на какую максимальную высоту поднимается брусок.

Answer 1

Дано: m1=10г=0,01 кг, M=200г=0,2кг, v1=100м/с, v2=50м/сНайти: h-?найдем энергия отданную брускуEк = m1v^2 / 2Eк = 0,01кг*(100м/с-50м/с)^2 / 2 = 25 Дж Eк=Eп Eп=M*g*hh = Eп / m2*gh = 25 Дж / 0,2кг*10м/с^2 = 12,5 м.

Answer 2

Problem Analysis

We are given a bullet with a mass of 10 g that is flying horizontally and hits a wooden block with a mass of 200 g, which is suspended by a long string. The bullet's velocity changes from 100 m/s to 50 m/s upon impact. We need to determine the maximum height to which the block rises, neglecting any displacement of the block during the impact.

Solution

To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the bullet is equal to its final momentum after the collision with the block. We can express this as:

Initial momentum of the bullet = Final momentum of the bullet + Final momentum of the block

The momentum of an object is given by the product of its mass and velocity. Therefore, we can write:

m_bullet * v_initial_bullet = m_bullet * v_final_bullet + m_block * v_final_block

Since the bullet's mass remains constant, we can simplify the equation to:

v_initial_bullet = v_final_bullet + (m_block / m_bullet) * v_final_block

We are given the initial and final velocities of the bullet, as well as the masses of the bullet and the block. We can substitute these values into the equation to find the final velocity of the block:

50 m/s = 100 m/s + (200 g / 10 g) * v_final_block

Simplifying the equation:

v_final_block = 50 m/s - 20 * v_final_block

Solving for v_final_block:

21 * v_final_block = 50 m/s

v_final_block = 50 m/s / 21

Now that we have the final velocity of the block, we can use the principle of conservation of mechanical energy to determine the maximum height to which the block rises. The change in potential energy of the block is equal to the work done on it by the bullet. We can express this as:

Change in potential energy = Work done on the block

The change in potential energy is given by the product of the mass of the block, the acceleration due to gravity, and the change in height. The work done on the block is given by the product of the force applied by the bullet and the displacement of the block. Since the bullet is moving horizontally, the displacement of the block is zero. Therefore, the work done on the block is zero.

m_block * g * h = 0

Simplifying the equation:

h = 0

This means that the block does not rise at all. The bullet's impact does not cause the block to move vertically.

Answer

The block does not rise at all due to the impact of the bullet.