Question

Две тележки массами m1 и m2 движутся навстречу другу со скоростью v1=36 и v2=54. определить v тележек после неупругого столкновения.

Answer 1

Импульс системы двух тел до столкновения: P0 = m1v1+m2v2
После: P1 = (m1+m2)u, u - скорость после столкновения.
Из закона сохранения импульса: P0 = P1, тогда:
u = (m1*v1+m2*v2)/(m1+m2) 

Answer 2

Problem Analysis

We have two carts with masses m1 and m2 moving towards each other with velocities v1 and v2 respectively. After an inelastic collision, we need to determine the final velocity v of the carts.

Solution

To solve this problem, we can apply 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 initial momentum of the first cart (m1) is m1 * v1, and the initial momentum of the second cart (m2) is m2 * v2.

After the collision, the two carts stick together and move with a common final velocity v. Therefore, the final momentum of the combined carts is (m1 + m2) * v.

Since momentum is conserved, we can equate the initial momentum to the final momentum:

m1 * v1 + m2 * v2 = (m1 + m2) * v

Now we can solve this equation for v to find the final velocity of the carts.

Calculation

Let's substitute the given values into the equation and calculate the final velocity v.

Given: m1 = 1 m2 = 2 v1 = 36 v2 = 54

Using the equation m1 * v1 + m2 * v2 = (m1 + m2) * v, we can substitute the values:

1 * 36 + 2 * 54 = (1 + 2) * v

36 + 108 = 3 * v

144 = 3 * v

v = 144 / 3

v = 48

Answer

After the inelastic collision, the final velocity of the two carts is 48.

Explanation

When two objects collide inelastically, they stick together and move with a common final velocity. In this case, the two carts with masses m1 = 1 and m2 = 2 collide with velocities v1 = 36 and v2 = 54 respectively. After the collision, the carts stick together and move with a final velocity of 48. This is determined by applying the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.