Question

Два шара 1 и 2 одинакового размера с массой равной m1 и m2 столкнулись на горизонтальной поверхности лоб в лоб так, что шар 2 остановился, а шар 1 приобрел скорость v, утроив свою первоначальную скорость. Чему была ровна скорость v2 шара 2 до столкновения?

Answer 1

Решаем используя закон сохранения импульса.
Общий импульс до удара:
m₁v₁-m₂v₂
Знак минус ставим потому, что он движется в другую сторону
Общий импульс после удара:
-m₁*3v₁
m₁v₁-m₂v₂=-3m₁v₁ 
4m₁v₁=m₂v₂
v₂=4m₁v₁/m₂

Answer 2

Problem Analysis

We are given two spheres, 1 and 2, with the same size and masses m1 and m2, respectively. Sphere 2 comes to a stop after a head-on collision with sphere 1, while sphere 1 acquires a velocity v, three times its initial velocity. We need to determine the velocity v2 of sphere 2 before the collision.

Solution

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

The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of sphere 1 before the collision is m1 * v1, and the momentum of sphere 2 before the collision is m2 * v2.

After the collision, sphere 1 acquires a velocity v, three times its initial velocity. Therefore, its final velocity is 3 * v1.

Since sphere 2 comes to a stop after the collision, its final velocity is 0.

Using the principle of conservation of momentum, we can write the equation:

m1 * v1 + m2 * v2 = m1 * (3 * v1) + m2 * 0

Simplifying the equation, we get:

m1 * v1 + m2 * v2 = 3 * m1 * v1

Rearranging the equation to solve for v2, we have:

v2 = 3 * v1 - v1

Simplifying further, we get:

v2 = 2 * v1

Therefore, the velocity v2 of sphere 2 before the collision is twice the initial velocity v1 of sphere 1.

Answer

The velocity v2 of sphere 2 before the collision is twice the initial velocity v1 of sphere 1.