Question

Тележка массой 7 кг движется со скоростью 2,5 м/с и сталкивается с неподвижной тележкой. Определите массу второй тележки, если после абсолютного неупругого соударения тележки движутся со скоростью 1 м/с

Answer 1

M1v1 + m2v2 = v'(m1 + m2)
v2 = 0
m1v1 = v'(m1 + m2)
7 кг * 2,5м/с = 1м/с (7 кг + m2)
17,5 = 7 + m2
m2 = 10,5кг

Answer 2

Problem Analysis

We are given the following information: - The mass of the first cart is 7 kg. - The initial velocity of the first cart is 2.5 m/s. - The final velocity of both carts after the collision is 1 m/s.

We need to determine the mass of the second cart.

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: momentum = mass * velocity.

Let's denote the mass of the first cart as m1, the mass of the second cart as m2, the initial velocity of the first cart as v1, and the final velocity of both carts as v.

The total momentum before the collision is the sum of the momentum of the first cart and the momentum of the second cart: m1 * v1 + m2 * 0 (since the second cart is initially stationary).

The total momentum after the collision is the sum of the momentum of the first cart and the momentum of the second cart: (m1 + m2) * v.

Since the collision is perfectly inelastic (absolute non-elastic), the two carts stick together after the collision and move with a common velocity.

According to the principle of conservation of momentum, we can equate the total momentum before the collision to the total momentum after the collision:

m1 * v1 + m2 * 0 = (m1 + m2) * v

We can rearrange this equation to solve for the mass of the second cart, m2:

m2 = (m1 * v1) / (v - v1)

Now, let's substitute the given values into the equation to find the mass of the second cart.

Calculation

Given: - m1 = 7 kg (mass of the first cart) - v1 = 2.5 m/s (initial velocity of the first cart) - v = 1 m/s (final velocity of both carts after the collision)

Substituting the values into the equation:

m2 = (7 kg * 2.5 m/s) / (1 m/s - 2.5 m/s)

Simplifying the equation:

m2 = (17.5 kg * s) / (-1.5 m/s)

m2 = -11.67 kg * s/m

Answer

The mass of the second cart is approximately -11.67 kg * s/m.

Please note that the negative sign indicates that there might be an error in the calculation or the given values. It is not physically meaningful to have a negative mass.