Question

Две частицы массами m1=4,8г и m2=7,2г двигались по взаимно перпендикулярным направлениям. Модуль скорости первой частицы u1=1,0 м/с, модуль скорости второй u2=0,50 м/с. После абсолютно неупругого столкновения частицы движутся вместе. Определите модуль скорости частиц после столкновения.

Answer 1

Количество движения до столкновения равно ему после соударения, учтем это вектора. Обозначим их vx;vy
4.8*1.0=(m1+m2)vx   vx=4.8/12 = 0.4
  7.2*0.5=12*vy   vy=7.2*0.5/12 = 0.3
легко найти и общий модуль скорости √0,4²+0,3²=√0,16+0,09=√0,25=0,5м/с

Answer 2

Problem Analysis

We are given two particles with masses m1 = 4.8 g and m2 = 7.2 g, moving in perpendicular directions. The magnitude of the velocity of the first particle is u1 = 1.0 m/s, and the magnitude of the velocity of the second particle is u2 = 0.50 m/s. After an inelastic collision, the particles move together. We need to determine the magnitude of their velocity 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 a particle is given by the product of its mass and velocity: p = m * v.

Before the collision, the total momentum is the sum of the individual momenta of the particles:

p_total_before = p1_before + p2_before

After the collision, the particles move together, so they have a common velocity. The total momentum after the collision is the sum of the individual momenta of the particles:

p_total_after = (m1 + m2) * v_after

Since momentum is conserved, we can equate the total momentum before the collision to the total momentum after the collision:

p_total_before = p_total_after

Substituting the expressions for the individual momenta and solving for v_after, we can find the magnitude of the velocity of the particles after the collision.

Let's calculate it step by step.

Step 1: Calculate the total momentum before the collision

The momentum of a particle is given by the product of its mass and velocity: p = m * v.

The momentum of the first particle before the collision is:

p1_before = m1 * u1

The momentum of the second particle before the collision is:

p2_before = m2 * u2

The total momentum before the collision is the sum of the individual momenta:

p_total_before = p1_before + p2_before

Step 2: Calculate the total momentum after the collision

The total momentum after the collision is given by:

p_total_after = (m1 + m2) * v_after

Step 3: Equate the total momentum before and after the collision

Since momentum is conserved, we can equate the total momentum before the collision to the total momentum after the collision:

p_total_before = p_total_after

Substituting the expressions for the individual momenta and solving for v_after, we get:

p1_before + p2_before = (m1 + m2) * v_after

Step 4: Calculate the magnitude of the velocity after the collision

Substituting the given values into the equation, we can solve for v_after:

(m1 * u1) + (m2 * u2) = (m1 + m2) * v_after

Now we can substitute the given values and calculate the magnitude of the velocity after the collision.

Calculation:

m1 = 4.8 g = 0.0048 kg m2 = 7.2 g = 0.0072 kg u1 = 1.0 m/s u2 = 0.50 m/s

Substituting the values into the equation:

(0.0048 kg * 1.0 m/s) + (0.0072 kg * 0.50 m/s) = (0.0048 kg + 0.0072 kg) * v_after

0.0048 kg + 0.0036 kg = 0.012 kg * v_after

0.0084 kg = 0.012 kg * v_after

Dividing both sides by 0.012 kg:

v_after = 0.0084 kg / 0.012 kg

v_after = 0.7 m/s

Answer:

The magnitude of the velocity of the particles after the collision is 0.7 m/s.