Question

Шарик, летевший со скоростью 20 м/с, после лобового упругого столкновения с неподвижным кубом продолжил двигаться в том же направлении со скоростью 10 м/с. Определите во сколько раз масса шарика больше массы куба.

Answer 1

M масса шарика
М масса куба
из закона сохранения импульса mv1=mv2+Mu
MU=mv1mv2=20m-10m=
10m
тк MU=10m то M^2*U^2=100m^2
отсюда U^2=100m^2/M^2
при упругом ударе сохраняется кинетическая энергия
E1=mv1^2/2=m*400/2=
200m - энергия до удара
Е2=mv2^2/2=m*100/2=
50m-энергия шарика после удара
значит Е=Е1-Е2=150m
энергия куба
с другой стороны
150m=MU^2/2
значит 300m=MU^2
Подставим U^2
300m=M*100m^2/M^2
3M=m
ответ в 3 раза

Answer 2

Calculation of the Mass Ratio

To determine the mass ratio between the ball and the cube after the elastic collision, 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 calculated by multiplying its mass by its velocity. Therefore, we can write the equation for the conservation of momentum as follows:

Initial momentum = Final momentum

The initial momentum is the product of the mass of the ball and its initial velocity, while the final momentum is the sum of the products of the masses and velocities of the ball and the cube after the collision.

Let's denote the mass of the ball as m and the mass of the cube as M. The initial velocity of the ball is 20 m/s, and the final velocity of both the ball and the cube after the collision is 10 m/s.

Using the conservation of momentum equation, we can write:

m * 20 = (m + M) * 10

Simplifying the equation, we get:

20m = 10m + 10M

Subtracting 10m from both sides of the equation, we have:

10m = 10M

Dividing both sides of the equation by 10, we get:

m = M

Therefore, the mass of the ball is equal to the mass of the cube. The mass ratio between the ball and the cube is 1:1.

To summarize, the mass of the ball is equal to the mass of the cube after the elastic collision. The mass ratio between the ball and the cube is 1:1.