Question

Мяч массой 1,5 кг летевший со скоростью 5м/с попадает в неподвижную тележку с пюпечком массой 5кг и закрывает в нем. Найти их скорость после

Answer 1

По закону сохранения импульс: m1v1+m2v2=v(m1+m2), тк тележка не подвижна, т.е V2=0 м/c, получаем
m1v1=v(m1+m2)
v= m1v1/(m1+m2)
v = 1,5*5/(5+1,5)= 1,15 м/с

Answer 2

Calculation of Final Velocity

To find the final velocity of the ball and the cart after the 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 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 of the object - v is the velocity of the object

Let's denote the mass of the ball as m1 (1.5 kg) and its initial velocity as v1 (5 m/s). The mass of the cart with the puppet is m2 (5 kg). We need to find the final velocity of both the ball and the cart after the collision, denoted as v1' and v2' respectively.

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

m1 * v1 + m2 * 0 = m1 * v1' + m2 * v2'

Since the cart is initially at rest (0 m/s), its initial momentum is zero.

Simplifying the equation, we get:

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

Now we can substitute the given values into the equation and solve for v1':

1.5 kg * 5 m/s = 1.5 kg * v1' + 5 kg * v2'

Calculation

Substituting the values into the equation:

7.5 kg m/s = 1.5 kg * v1' + 5 kg * v2'

To solve for v1' and v2', we need an additional equation. The coefficient of restitution (e) can be used to relate the velocities of the ball and the cart after the collision. The coefficient of restitution is a measure of how "bouncy" the collision is. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach.

Mathematically, the coefficient of restitution (e) is given by:

e = (v2' - v1') / (v1 - v2)

Where: - e is the coefficient of restitution - v1 is the initial velocity of the ball - v2 is the initial velocity of the cart - v1' is the final velocity of the ball - v2' is the final velocity of the cart

In this case, since the cart is initially at rest, v2 is 0 m/s. The coefficient of restitution can be rearranged to solve for v2':

v2' = e * (v1 - v2) + v1'

Substituting the given values into the equation:

v2' = e * (5 m/s - 0 m/s) + v1'

Now we have two equations:

7.5 kg m/s = 1.5 kg * v1' + 5 kg * v2' v2' = e * (5 m/s - 0 m/s) + v1'

We can solve these equations simultaneously to find the values of v1' and v2'.

Solution

Unfortunately, the coefficient of restitution (e) is not provided in the question. Without this information, we cannot determine the exact values of v1' and v2'. The coefficient of restitution depends on the nature of the collision and the materials involved. It can range from 0 (perfectly inelastic collision) to 1 (perfectly elastic collision).

If you have the value of the coefficient of restitution (e), please provide it so that we can calculate the final velocities of the ball and the cart after the collision.