Question

Пожалуйста!!!!!Помогите!!!!! Пуля, летящая со скоростью 100м/с под углом 60° к горизонту ,врезается в покоящийся брусок на горизонтальной плоскости массой в 9раз превышающей массу пули.Какое расстояние пройдёт брусок по поверхности, если коэффициент трения равен 0,5 ,к моменту когда скорость бруска уменьшится на 20%.

Answer 1

Используем закон сохранения импульса
импульс системы до удара m₁ * v * cos α = m * v * cos α / 9
импульс системы после соударения (m / 9 + m) * v₁
составим уравнение и выразим скорость системы после соударения
m * v * cos α / 9 = (m / 9 + m) * v₁
v₁ = m * v * cos α / (9 * 10 * m / 9) = v * cos α /10
после соударения система движется под действием силы трения
составим уравнение динамики ( 2 закон Ньютона)
F = 10 * m * a / 9 = - μ * 10 * m * g / 9 => a = - μ * g
выразим ускорение из уравнения кинематики
v₂² - v₁² = 2 * a * S, где v₂ = 0,2 * v₁ = 0,2 * v * cos α /10 = 0,02 * v * cos α
(0,02 * v * cos α)² - (0,1 * v * cos α)² = 2 * a * S
0,0004 * v² * cos²α - 0,01 v² * cos²α = - 2 * μ * g *S
- 0,0096 v² * cos²α = - 2 *μ * g * S
0,0096 * v² * cos²α = 2 * μ * g * S => S = 0,0096 * v² * cos²α / (2 *μ * g)
S = 0,0096 * (100 м/с)² * cos²(60°) / (2 * 0,5 * 9,8 м/с²) = 0,0096 * 10⁴ * 0,5² / 9,8 м/с² = 2,4 м

Answer 2

Calculation of the Distance Traveled by the Block

To calculate the distance traveled by the block after the bullet hits it, we need to consider the conservation of momentum and the work done by friction.

1. Conservation of Momentum: - Before the collision, the bullet has momentum in the horizontal direction, given by p_bullet = m_bullet * v_bullet * cos(theta), where m_bullet is the mass of the bullet, v_bullet is the velocity of the bullet, and theta is the angle the bullet makes with the horizontal. - After the collision, the bullet and the block move together with a common velocity, v_final. - The momentum of the bullet and the block after the collision is given by p_final = (m_bullet + m_block) * v_final.

2. Work Done by Friction: - The work done by friction is equal to the force of friction multiplied by the distance traveled. - The force of friction is given by F_friction = mu * m_block * g, where mu is the coefficient of friction, m_block is the mass of the block, and g is the acceleration due to gravity. - The distance traveled by the block is given by d = work / F_friction, where work is the work done by friction.

To find the distance traveled by the block, we need to calculate the final velocity of the bullet and block after the collision and then determine the work done by friction.

Calculation Steps:

1. Calculate the final velocity of the bullet and block after the collision: - Since momentum is conserved, we can equate the initial momentum of the bullet to the final momentum of the bullet and block: ``` m_bullet * v_bullet * cos(theta) = (m_bullet + m_block) * v_final ``` - Rearranging the equation, we can solve for v_final: ``` v_final = (m_bullet * v_bullet * cos(theta)) / (m_bullet + m_block) ```

2. Calculate the work done by friction: - The work done by friction is given by work = F_friction * d. - Rearranging the equation, we can solve for d: ``` d = work / F_friction ```

3. Substitute the given values into the equations and calculate the distance traveled by the block.

Let's perform the calculations.

Calculation:

Given: - Velocity of the bullet, v_bullet = 100 m/s - Angle of the bullet with the horizontal, theta = 60° - Coefficient of friction, mu = 0.5 - Mass of the block, m_block = 9 * mass of the bullet

We can calculate the final velocity of the bullet and block after the collision using the equation: ``` v_final = (m_bullet * v_bullet * cos(theta)) / (m_bullet + m_block) ``` where m_bullet is the mass of the bullet.

Let's calculate the final velocity of the bullet and block:

1. Calculate the mass of the bullet: - Let's assume the mass of the bullet is m_bullet. - Since the mass of the block is 9 times the mass of the bullet, we have m_block = 9 * m_bullet.

2. Calculate the final velocity: - Substituting the values into the equation, we have: ``` v_final = (m_bullet * v_bullet * cos(theta)) / (m_bullet + m_block) = (m_bullet * 100 * cos(60°)) / (m_bullet + 9 * m_bullet) = (m_bullet * 100 * 0.5) / (10 * m_bullet) = 5 m/s ```

Now, let's calculate the distance traveled by the block using the equation: ``` d = work / F_friction ``` where work is the work done by friction and F_friction is the force of friction.

3. Calculate the work done by friction: - The force of friction is given by F_friction = mu * m_block * g, where g is the acceleration due to gravity. - The work done by friction is given by work = F_friction * d.

Let's calculate the distance traveled by the block:

1. Calculate the force of friction: - Substituting the values into the equation, we have: ``` F_friction = mu * m_block * g = 0.5 * (9 * m_bullet) * g = 4.5 * m_bullet * g ```

2. Calculate the distance traveled by the block: - Substituting the values into the equation, we have: ``` d = work / F_friction = (F_friction * d) / F_friction = d ```

Therefore, the distance traveled by the block is equal to the work done by friction.

Please note that we need the mass of the bullet to proceed with the calculations. If you have the mass of the bullet, please provide it so that we can continue with the calculations.