Question

Ракета, летящей со скоростью v разогналась до вдвое большей скорости. В результате сгорания топлива полная масса ракеты уменьшилась вдвое по сравнению с ее массой в начале разгона. Во сколько раз изменилась при этом кинетическая энергия ракеты?

Answer 1

E1=m*v^2/2

E2=m/2*(2v)^2/2=4*m*v^2/4=m*v^2

E2/E1=(m*v^2)/(m*v^2/2)=2.

Ответ: Кинетическая энергия увеличилась в 2 раза.

Answer 2

Calculation of the Change in Kinetic Energy of the Rocket

To calculate the change in kinetic energy of the rocket, we need to consider the initial and final velocities of the rocket, as well as the change in mass.

Given: - The rocket initially travels at a velocity of v. - The rocket's velocity doubles during its acceleration. - The rocket's mass decreases by half due to fuel consumption.

We can use the formula for kinetic energy (KE) to calculate the change in kinetic energy:

KE = (1/2) * m * v^2

Let's break down the calculation step by step:

1. Initial kinetic energy (KE1): - Mass of the rocket at the beginning = m - Velocity of the rocket at the beginning = v - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - Mass of the rocket after fuel consumption = m/2 - Velocity of the rocket after acceleration = 2v - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Now, let's substitute the given values and calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half and its velocity doubles, we can substitute these values into the equations:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Let's calculate the change in kinetic energy of the rocket.

Calculation:

1. Initial kinetic energy (KE1): - KE1 = (1/2) * m * v^2

2. Final kinetic energy (KE2): - KE2 = (1/2) * (m/2) * (2v)^2

3. Change in kinetic energy (ΔKE): - ΔKE = KE2 - KE1

Given that the rocket's mass decreases by half