Question

две тележки 100 и 200 грамм соединили сжатой пружиной, которая в этом состоянии удерживается нитью.После того как нить пережи , пружина распрямилась и тележки разъехались. Тележка меньшей массы приобрела скорость 0,5 м/с. какую скорость приобрела вторая тележка?

Answer 1

Дано: m₁ = 0.1 кг, m₂ = 0.2 кг, U₁ = 0.5 м/с

Найти: U₂ - ?

Решение:

$p_{1} + p_{2} = p_{1}' + p_{2}' \\ \\ 0 = m_{1}\upsilon_{1} + m_{2}\upsilon_{2} \\ \\ OX: m_{1}\upsilon_{1} = m_{2}\upsilon_{2} \ ; \ \upsilon_{2} = \dfrac{m_{1}\upsilon_{1}}{m_{2}} \\ \\ \upsilon_{2} = \dfrac{0.1 * 0.5}{0.2} = 0.25 \ [\frac{M}{C}]$

Ответ: U₂ = 0.25 м/с

Answer 2

Problem Analysis

We have two carts with masses of 100 grams and 200 grams, respectively. These carts are connected by a compressed spring, which is held in place by a string. When the string is released, the spring straightens out and the carts move apart. We are given that the cart with the smaller mass acquires a velocity of 0.5 m/s. We need to determine the velocity acquired by the second cart.

Solution

To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the string is released is equal to the total momentum after the string is released.

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

Initial momentum = Final momentum

The initial momentum is the sum of the momentum of the two carts before the string is released, and the final momentum is the sum of the momentum of the two carts after the string is released.

Let's denote the mass of the first cart as m1 (100 grams) and the mass of the second cart as m2 (200 grams). The initial velocity of the first cart is 0 m/s, and the initial velocity of the second cart is also 0 m/s. The final velocity of the first cart is 0.5 m/s, and we need to find the final velocity of the second cart, which we'll denote as v2.

Using the conservation of momentum equation, we can write:

m1 * 0 + m2 * 0 = m1 * 0.5 + m2 * v2

Since the initial velocities are both 0, the left side of the equation becomes 0. Therefore, we can simplify the equation to:

0 = m1 * 0.5 + m2 * v2

Solving for v2, we get:

v2 = - (m1 * 0.5) / m2

Substituting the values of m1 (100 grams) and m2 (200 grams) into the equation, we can calculate the final velocity of the second cart.

Calculation

Let's calculate the final velocity of the second cart using the given masses:

m1 = 100 grams = 0.1 kg m2 = 200 grams = 0.2 kg

v2 = - (0.1 kg * 0.5 m/s) / 0.2 kg

v2 = - 0.05 m/s

Therefore, the final velocity of the second cart is -0.05 m/s.

Conclusion

After the string is released, the first cart with a mass of 100 grams acquires a velocity of 0.5 m/s, while the second cart with a mass of 200 grams acquires a velocity of -0.05 m/s. The negative sign indicates that the second cart moves in the opposite direction to the first cart.