Question

Два неупругих тела ,масса которых 4 и 6 кг,движутся навстречу друг другу со скоростями 3м в с каждое.Определить модуль и направление скорости каждого из этих тел после удара

Answer 1

По закону сохранения импульса  m1v1 + m2v2 = V(m1+m2) Это надо написать с векторами наверху у скоростей - это векторная запись закона.

Затем написать уравнение с учетом проекций  m1v1 - m2v2 = V(m1+m2)

V = m1v2 - m2v2 / (m1+m2)  V = 4*3 - 6*3 / (4+6) = - 0,6 (м/с)

Ответ: движется в сторону второго тела сос скоростью 0,6 м/с

Answer 2

Импульс более лёгкого тела 

 

P1=m1*v1=4*3=12

 

Импульс более тяжёлого тела 

 

P2=m2*v2=6*3=18

 

Векторы противо направлены, значит импульс системы тел, которая будет двигаться в сторону более тяжёлого, будет

 

18-12=6

 

Скорость такой системы будет

 

P=m*v

 

v=P/m

 

v=6/(4+6)=0,6 м/с

Answer 3

Problem Analysis

We are given two objects with masses of 4 kg and 6 kg, moving towards each other with velocities of 3 m/s each. We need to determine the magnitude and direction of the velocity of each object after 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: momentum = mass * velocity.

Let's denote the mass of the first object as m1, the mass of the second object as m2, the velocity of the first object before the collision as v1, and the velocity of the second object before the collision as v2.

The total momentum before the collision is given by: total momentum before = m1 * v1 + m2 * v2.

After the collision, the objects will exchange velocities, but the total momentum will remain the same. Therefore, the total momentum after the collision is also equal to: total momentum after = m1 * v1' + m2 * v2', where v1' and v2' are the velocities of the first and second objects after the collision, respectively.

Since the total momentum before and after the collision is the same, we can set up the following equation: m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'.

We can rearrange this equation to solve for v1' and v2': v1' = (m1 * v1 + m2 * v2 - m2 * (v2 - v1)) / (m1 + m2) and v2' = (m1 * v1 + m2 * v2 - m1 * (v1 - v2)) / (m1 + m2).

Now, let's substitute the given values into these equations and calculate the velocities after the collision.

Calculation

Given: - m1 = 4 kg (mass of the first object) - m2 = 6 kg (mass of the second object) - v1 = 3 m/s (velocity of the first object before the collision) - v2 = -3 m/s (velocity of the second object before the collision, negative because it is moving in the opposite direction)

Using the equations derived above, we can calculate the velocities after the collision:

v1' = (m1 * v1 + m2 * v2 - m2 * (v2 - v1)) / (m1 + m2) = (4 * 3 + 6 * (-3) - 6 * (3 - (-3))) / (4 + 6) = -1.2 m/s

v2' = (m1 * v1 + m2 * v2 - m1 * (v1 - v2)) / (m1 + m2) = (4 * 3 + 6 * (-3) - 4 * (3 - (-3))) / (4 + 6) = -4.8 m/s

Answer

After the collision, the magnitude and direction of the velocities of the two objects are as follows: - The first object has a velocity of 1.2 m/s in the opposite direction of its initial velocity. - The second object has a velocity of 4.8 m/s in the opposite direction of its initial velocity.

Please note that the negative sign indicates the opposite direction of the initial velocities.