Question

Шарик массой 50 г., движущийся со скоростью 10 м/с ударяется о вертикальную стенку под углом 45 градусов к ней и отскакивает без потери скорости (абсолютно упругий удар). Найти изменение импульса шарика.

Answer 1

Ответ:

Объяснение:

Δp = 2·m·V·cos α

Δp = 2·0,050·10·√2 / 2 = 0,5·√2 ≈ 0,71 кг·м/с

Answer 2

Calculation of Change in Momentum

To find the change in momentum of the ball, we need to calculate the initial and final momentum of the ball.

The momentum of an object is given by the product of its mass and velocity. Mathematically, it can be expressed as:

Momentum (p) = mass (m) × velocity (v)

Given information: - Mass of the ball (m) = 50 g = 0.05 kg - Initial velocity of the ball (u) = 10 m/s - Angle of impact with the wall (θ) = 45 degrees

To calculate the initial momentum (p_initial), we need to find the horizontal and vertical components of the initial velocity.

The horizontal component of the initial velocity (u_x) can be calculated using the formula:

u_x = u × cos(θ)

Substituting the given values, we have:

u_x = 10 m/s × cos(45°)

To calculate the vertical component of the initial velocity (u_y), we can use the formula:

u_y = u × sin(θ)

Substituting the given values, we have:

u_y = 10 m/s × sin(45°)

Now, we can calculate the initial momentum (p_initial) using the horizontal and vertical components of the initial velocity:

p_initial = m × u_x + m × u_y

Substituting the given values, we have:

p_initial = 0.05 kg × (10 m/s × cos(45°)) + 0.05 kg × (10 m/s × sin(45°))

To calculate the final momentum (p_final), we need to consider that the ball rebounds from the wall with the same speed and angle of incidence. Therefore, the final velocity (v) will have the same magnitude as the initial velocity (u), but the direction will be opposite.

The horizontal component of the final velocity (v_x) can be calculated using the formula:

v_x = -u × cos(θ)

Substituting the given values, we have:

v_x = -10 m/s × cos(45°)

To calculate the vertical component of the final velocity (v_y), we can use the formula:

v_y = u × sin(θ)

Substituting the given values, we have:

v_y = 10 m/s × sin(45°)

Now, we can calculate the final momentum (p_final) using the horizontal and vertical components of the final velocity:

p_final = m × v_x + m × v_y

Substituting the given values, we have:

p_final = 0.05 kg × (-10 m/s × cos(45°)) + 0.05 kg × (10 m/s × sin(45°))

Finally, we can calculate the change in momentum (Δp) by subtracting the initial momentum from the final momentum:

Δp = p_final - p_initial

Substituting the calculated values, we have:

Δp = (0.05 kg × (-10 m/s × cos(45°)) + 0.05 kg × (10 m/s × sin(45°))) - (0.05 kg × (10 m/s × cos(45°)) + 0.05 kg × (10 m/s × sin(45°)))

Simplifying the equation, we can find the change in momentum of the ball.

Please note that the above calculations assume an ideal scenario of an elastic collision, where there are no energy losses during the collision.

Let me calculate the change in momentum for you.