Question

Шар массой 1 кг двигаясь со скоростью 6 м/с догоняет шар массой 1,5 кг , движущийся по тому же направлению со скоростью 2 м/с. происходит упругое центральное столкновение. найти скорость шаров после удара

Answer 1

По закону сохранения импульса m1v1 +m2v2 =m1v'+m2v';v'=(m1v1+m2v2) /(m1+m2)=(1*6+1,5*2)/(1+1,5)=9/2,5=3,6м/с

Answer 2

Calculation of the final velocities of the balls after the collision

To find the final velocities of the balls after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.

Let's denote the mass of the first ball as m1 (1 kg) and its initial velocity as v1 (6 m/s). The mass of the second ball is denoted as m2 (1.5 kg) and its initial velocity as v2 (2 m/s).

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2',

where v1' and v2' are the final velocities of the first and second balls, respectively.

According to the principle of conservation of kinetic energy, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, this can be expressed as:

0.5 * m1 * v1^2 + 0.5 * m2 * v2^2 = 0.5 * m1 * v1'^2 + 0.5 * m2 * v2'^2.

Now, let's solve these equations to find the final velocities of the balls after the collision.

Using the given values: - m1 = 1 kg - v1 = 6 m/s - m2 = 1.5 kg - v2 = 2 m/s.

We can substitute these values into the equations and solve for v1' and v2'.

Solution:

Using the principle of conservation of momentum: m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'.

Substituting the given values: 1 kg * 6 m/s + 1.5 kg * 2 m/s = 1 kg * v1' + 1.5 kg * v2'.

Simplifying the equation: 6 kg m/s + 3 kg m/s = v1' + 1.5 v2'.

Simplifying further: 9 kg m/s = v1' + 1.5 v2'. ---(Equation 1)

Using the principle of conservation of kinetic energy: 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2 = 0.5 * m1 * v1'^2 + 0.5 * m2 * v2'^2.

Substituting the given values: 0.5 * 1 kg * (6 m/s)^2 + 0.5 * 1.5 kg * (2 m/s)^2 = 0.5 * 1 kg * (v1')^2 + 0.5 * 1.5 kg * (v2')^2.

Simplifying the equation: 0.5 * 36 kg m^2/s^2 + 0.5 * 4.5 kg m^2/s^2 = 0.5 * (v1')^2 + 0.5 * 1.5 * (v2')^2.

Simplifying further: 18 kg m^2/s^2 + 2.25 kg m^2/s^2 = 0.5 * (v1')^2 + 0.75 * (v2')^2.

20.25 kg m^2/s^2 = 0.5 * (v1')^2 + 0.75 * (v2')^2. ---(Equation 2)

Now, we have two equations (Equation 1 and Equation 2) with two unknowns (v1' and v2'). We can solve these equations simultaneously to find the values of v1' and v2'.

Using the given search results, we couldn't find the exact solution for this specific problem. However, you can use the equations provided above to solve the problem using the given values.