Question

Два пластилиновых шара катятся на встречу друг к другу их скорость равна 1 м/c масса более лёгкого шара равна 10 грамм известно что их скорость после с столкновения стала 0,5м/c . чему равна масса 2 шара ?

Answer 1

Problem Analysis

We are given two clay balls rolling towards each other. The speed of both balls is 1 m/s. The mass of the lighter ball is 10 grams. After the collision, the speed of both balls becomes 0.5 m/s. We need to find the mass of the second ball.

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 of the object, - m is the mass of the object, and - v is the velocity of the object.

Before the collision, the momentum of the first ball is given by:

p1 = m1 * v1

where: - p1 is the momentum of the first ball, - m1 is the mass of the first ball, and - v1 is the velocity of the first ball.

Similarly, the momentum of the second ball before the collision is given by:

p2 = m2 * v2

where: - p2 is the momentum of the second ball, - m2 is the mass of the second ball, and - v2 is the velocity of the second ball.

After the collision, the momentum of the first ball is given by:

p1' = m1 * v1'

where: - p1' is the momentum of the first ball after the collision, and - v1' is the velocity of the first ball after the collision.

Similarly, the momentum of the second ball after the collision is given by:

p2' = m2 * v2'

where: - p2' is the momentum of the second ball after the collision, and - v2' is the velocity of the second ball after the collision.

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

p1 + p2 = p1' + p2'

Substituting the expressions for momentum, we get:

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

We are given the values of v1, v2, and v2'. We also know that v1' = v2' because the balls stick together after the collision and move with the same velocity. Therefore, we can rewrite the equation as:

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

Simplifying the equation, we get:

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

Rearranging the equation to solve for m2, we have:

m2 = (m1 * v1 + m2 * v2 - m1 * v1') / v1'

Substituting the given values, we can calculate the mass of the second ball.

Calculation

Given: - v1 = 1 m/s (velocity of the first ball before the collision) - v2 = -1 m/s (velocity of the second ball before the collision, as it is moving in the opposite direction) - v1' = v2' = 0.5 m/s (velocity of both balls after the collision) - m1 = 10 grams (mass of the first ball)

Using the equation derived above, we can calculate the mass of the second ball (m2):

m2 = (m1 * v1 + m2 * v2 - m1 * v1') / v1'

Substituting the given values:

m2 = (10 * 1 + m2 * (-1) - 10 * 0.5) / 0.5

Simplifying the equation:

2 * m2 = 10 - 5 - 10 * 0.5

2 * m2 = 5 - 5

2 * m2 = 0

m2 = 0 / 2

m2 = 0 grams

Therefore, the mass of the second ball is 0 grams.

Answer

The mass of the second ball is 0 grams.