Question

Два шара массами 1 кг и 2 к движутся во взаимно перпендикулярных направлениях со скоростями 3 м/с и 2 м/с соответственно,сталкиваясь.считая удар не упругим, определите кинетическую энергию шаров после удара

Answer 1

Поскольку столкновение не упругое, то выполняется закон сохранения импульса. Геометрическая сумма P1+P2 равна P12
P1=1·3=3
P2=2·2=4
P1+P2=sqrt(P1²+P2²)=5
P12=mvv=5/(1+2)=5/3
кинетическая энергия E=mv²/2
E=3·25/9/2=25/6=4.2 Дж

Answer 2

Calculation of Kinetic Energy after Collision

To determine the kinetic energy of the two spheres after the collision, we can use the principle of conservation of momentum. Since the collision is assumed to be inelastic, the total kinetic energy of the system will not be conserved.

The formula for the conservation of momentum is:

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

Where: - m1 and m2 are the masses of the spheres (1 kg and 2 kg, respectively) - v1 and v2 are the velocities of the spheres before the collision (3 m/s and 2 m/s, respectively) - v is the velocity of the spheres after the collision

Using the given values, we can substitute them into the equation to solve for v:

1 kg * 3 m/s + 2 kg * 2 m/s = (1 kg + 2 kg) * v

Simplifying the equation:

3 kg * 3 m/s + 4 kg * 2 m/s = 3 kg * v

9 kg m/s + 8 kg m/s = 3 kg * v

17 kg m/s = 3 kg * v

Dividing both sides of the equation by 3 kg:

v = 17 kg m/s / 3 kg

v ≈ 5.67 m/s

Now that we have the velocity of the spheres after the collision, we can calculate the kinetic energy using the formula:

Kinetic Energy = 0.5 * mass * velocity^2

For the first sphere with a mass of 1 kg:

Kinetic Energy1 = 0.5 * 1 kg * (5.67 m/s)^2

Kinetic Energy1 ≈ 16.12 J

For the second sphere with a mass of 2 kg:

Kinetic Energy2 = 0.5 * 2 kg * (5.67 m/s)^2

Kinetic Energy2 ≈ 64.48 J

Therefore, the kinetic energy of the first sphere after the collision is approximately 16.12 Joules, and the kinetic energy of the second sphere after the collision is approximately 64.48 Joules.