Question

СРОЧНО НАДО!!!! ДАЮ 35 БАЛЛОВ!!!!!! Человек массой 60 кг, бегущий со скоростью 36 км/ч, догоняет тележку, движущуюся со скоростью 2 м/с и вскакивает на неё. С какой скоростью станет двигаться тележка, если её масса 15 кг?А) Рассчитайте импульс человека. В) Запишите закон сохранения импульса после взаимодействияС) Рассчитайте импульс тележки и скорость, с которой будут двигаться вместе ​​

Answer 1

A.

Импульс p = mv

m₁ человека = 60 кг

v₁ человека = 36 км/ч = 10 м/с

p₁ человека = m₁v₁ = 10 * 60 = 600 (кг*м/с)

B.

Можно сказать, что запрыгивание человека в тележку — абсолютно неупругое столкновение, следовательно человек и тележка после вскакивания следует расматривать как одно единое тело.

Закон сохранения импульса для абсолютно неупругого столкновения:

m₁v₁+m₂v₂ = (m₁+m₂)v', где переменные с индексом 1 — человека, а с индексом 2 — тележки.

C.

m₂ тележки = 15 кг

v₂ тележки = 2 м/с

Импульс тележки: p₂ = m₂v₂ = 15 * 2 = 30 (кг*м/с)

Подставляем в предыдущее уравнение наши данные:

p₁+p₂ = (m₁+m₂)v'

600+30 = (60 + 15)v'

630 = 75v'

v' = 8,4 (м/с)

Answer 2

Calculation of the Speed of the Cart after Interaction

To calculate the speed of the cart after the person jumps onto it, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.

Let's denote the mass of the person as m1 (60 kg), the initial speed of the person as v1 (36 km/h), the mass of the cart as m2 (15 kg), and the final speed of the cart and person together as v.

To find the final speed of the cart, we can use the equation:

m1 * v1 + m2 * 0 = (m1 + m2) * v

Since the person jumps onto the cart, their initial speed relative to the cart is 0 m/s. Therefore, the momentum of the person before the interaction is m1 * v1, and the momentum of the cart before the interaction is 0.

Simplifying the equation, we have:

60 kg * (36 km/h) + 15 kg * 0 = (60 kg + 15 kg) * v

Now, let's convert the units to be consistent. We'll convert the speed from km/h to m/s:

36 km/h = 36,000 m/3,600 s = 10 m/s

Substituting the values into the equation:

60 kg * 10 m/s + 15 kg * 0 = (60 kg + 15 kg) * v

Simplifying further:

600 kg·m/s = 75 kg * v

Dividing both sides by 75 kg:

v = 600 kg·m/s / 75 kg = 8 m/s

Therefore, the speed of the cart after the person jumps onto it will be 8 m/s.

Calculation of the Impulse of the Person

The impulse of an object is defined as the change in momentum of the object. It can be calculated using the equation:

Impulse = m * Δv

where m is the mass of the object and Δv is the change in velocity.

In this case, the person's mass is 60 kg, and their initial velocity is 36 km/h (which we converted to 10 m/s). After jumping onto the cart, their final velocity is the same as the cart's velocity, which we calculated to be 8 m/s.

Therefore, the change in velocity is:

Δv = 8 m/s - 10 m/s = -2 m/s

(Note: The negative sign indicates a decrease in velocity.)

Substituting the values into the equation:

Impulse = 60 kg * (-2 m/s) = -120 kg·m/s

Therefore, the impulse of the person is -120 kg·m/s.

Conservation of Momentum

The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. In this case, the system consists of the person and the cart.

Before the interaction, the momentum of the person is m1 * v1 (60 kg * 10 m/s), and the momentum of the cart is 0 kg·m/s.

After the interaction, the momentum of the person and the cart together is (m1 + m2) * v (75 kg * 8 m/s).

Therefore, the law of conservation of momentum can be written as:

m1 * v1 + m2 * 0 = (m1 + m2) * v

Substituting the values:

60 kg * 10 m/s + 15 kg * 0 = 75 kg * 8 m/s

Simplifying:

600 kg·m/s = 600 kg·m/s

This equation shows that the total momentum before and after the interaction is the same, confirming the conservation of momentum.

Calculation of the Impulse of the Cart and the Final Velocity

To calculate the impulse of the cart, we can use the same equation as before:

Impulse = m * Δv

where m is the mass of the cart and Δv is the change in velocity.

In this case, the mass of the cart is 15 kg, and its initial velocity is 0 m/s. After the person jumps onto the cart, their final velocity is 8 m/s.

Therefore, the change in velocity is:

Δv = 8 m/s - 0 m/s = 8 m/s

Substituting the values into the equation:

Impulse = 15 kg * 8 m/s = 120 kg·m/s

Therefore, the impulse of the cart is 120 kg·m/s.

To calculate the final velocity of the cart, we can use the equation:

Impulse = m * Δv

Rearranging the equation to solve for Δv:

Δv = Impulse / m

Substituting the values:

Δv = 120 kg·m/s / 15 kg = 8 m/s

Therefore, the final velocity of the cart is 8 m/s.

Please note that the negative sign in the impulse of the person indicates a decrease in velocity, while the positive sign in the impulse of the cart indicates an increase in velocity.