Question

Куля масою 10 кг наздоганяє кулю масою 8 кг.Швидкість першої кулі до зіткнення становить 20 м/с,а другої-5м/с.Знайти швидкість другої кулі після зіткнення, якщо швидкість першої 10м/с?

Answer 1

Ответ: 17.5 м/с

Объяснение:

По закону сохранения испульса:

m1*v1+m2v2=m1v12+m2v22

10*20+8*5=10*10+V22*8

V22=17.5v/c

Answer 2

Problem Analysis

We are given two spheres, one with a mass of 10 kg and the other with a mass of 8 kg. The first sphere is moving towards the second sphere with a velocity of 20 m/s, while the second sphere is moving towards the first sphere with a velocity of 5 m/s. We need to find the velocity of the second sphere after the collision, given that the velocity of the first sphere is 10 m/s.

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. Mathematically, momentum (p) is defined as:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

Before the collision, the total momentum is the sum of the individual momenta of the two spheres. After the collision, the total momentum remains the same.

Let's denote the velocity of the second sphere after the collision as v2.

Calculation

Before the collision: - The momentum of the first sphere (m1 = 10 kg, v1 = 20 m/s) is given by p1 = m1 * v1. - The momentum of the second sphere (m2 = 8 kg, v2 = -5 m/s) is given by p2 = m2 * v2, where the negative sign indicates the opposite direction.

After the collision: - The momentum of the first sphere is still m1 * v1. - The momentum of the second sphere is m2 * v2.

According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

p1 + p2 = p1 + m2 * v2

Simplifying the equation:

m2 * v2 = p2

Now we can substitute the values and solve for v2.

Calculation Steps

1. Calculate the momentum of the first sphere before the collision: p1 = m1 * v1. 2. Calculate the momentum of the second sphere before the collision: p2 = m2 * v2. 3. Apply the conservation of momentum equation: p1 + p2 = p1 + m2 * v2. 4. Simplify the equation: m2 * v2 = p2. 5. Substitute the given values and solve for v2.

Let's perform the calculations.

Calculation Results

1. The momentum of the first sphere before the collision: p1 = 10 kg * 20 m/s = 200 kg·m/s. 2. The momentum of the second sphere before the collision: p2 = 8 kg * (-5 m/s) = -40 kg·m/s. 3. Applying the conservation of momentum equation: 200 kg·m/s + (-40 kg·m/s) = 200 kg·m/s + 8 kg * v2. 4. Simplifying the equation: -40 kg·m/s = 8 kg * v2. 5. Solving for v2: v2 = (-40 kg·m/s) / 8 kg = -5 m/s.

Answer

The velocity of the second sphere after the collision is -5 m/s.

Please note that the negative sign indicates that the second sphere is moving in the opposite direction after the collision.