Question

Пуля массой 9 г пробивает доску толщиной 5 см при этом его скорость убывает с 600метр в секунду до 200 метр в секунду. найдите изменение кинетической энергии и работу а также значение силы сопротивления, считая её постоянной величиной

Answer 1

1)По закону сохранения энергии: Ек0=Ек +Атр. ( Атр- работа силы трения) Атр=Ек0 - Ек. 
Атр=m*v0^2 / 2 - m*v^2 / 2. Aтр=m / 2*(v0^2 - v^2). Атр=9*10^(-3) / 2*(360000 - 40000)=1440Дж. 
Изменение кинетической энергии dЕк= - Атр. dЕк= - 1440Дж. Aтр=Fтр*S. ( S - толщина доски) . 
Fтр=Атр / S. Fтр= 1440 / 0,05=28800H. 
2)Полная энергия = сумме кинетической и потенциальной. 
Е=Ек +Еп. 
Ек=m*v^2 / 2. Еп=m*g*h. 
Ек=10^5*40000 / 2=2*10^9Дж. 
Еп=10^5*10*1000=10^9Дж. 
Е=3*10^9Дж.

Answer 2

Calculation of Change in Kinetic Energy and Work

To calculate the change in kinetic energy and work, we need to use the formula for kinetic energy and work.

The formula for kinetic energy is:

Kinetic Energy (KE) = (1/2) * mass * velocity^2

The formula for work is:

Work (W) = force * distance

In this case, we are given the mass of the bullet (9 g), the initial velocity (600 m/s), the final velocity (200 m/s), and the thickness of the board (5 cm).

To find the change in kinetic energy, we need to calculate the initial kinetic energy and the final kinetic energy, and then subtract the initial kinetic energy from the final kinetic energy.

To find the work done, we need to calculate the force exerted by the bullet on the board and then multiply it by the distance traveled by the bullet inside the board.

Let's calculate the change in kinetic energy and work step by step.

1. Calculation of Initial Kinetic Energy (KE_initial):

Using the formula for kinetic energy, we can calculate the initial kinetic energy of the bullet.

KE_initial = (1/2) * mass * velocity_initial^2

Substituting the given values:

KE_initial = (1/2) * 0.009 kg * (600 m/s)^2

2. Calculation of Final Kinetic Energy (KE_final):

Using the formula for kinetic energy, we can calculate the final kinetic energy of the bullet.

KE_final = (1/2) * mass * velocity_final^2

Substituting the given values:

KE_final = (1/2) * 0.009 kg * (200 m/s)^2

3. Calculation of Change in Kinetic Energy (ΔKE):

The change in kinetic energy is the difference between the final kinetic energy and the initial kinetic energy.

ΔKE = KE_final - KE_initial

4. Calculation of Force (F):

To calculate the force exerted by the bullet on the board, we can use Newton's second law of motion:

Force (F) = mass * acceleration

Since the bullet is decelerating, the acceleration is negative.

Acceleration = (velocity_final - velocity_initial) / time

The time can be calculated using the thickness of the board and the average velocity of the bullet inside the board.

time = distance / average_velocity

Substituting the given values:

time = 0.05 m / ((600 m/s + 200 m/s) / 2)

Now we can calculate the acceleration:

Acceleration = (200 m/s - 600 m/s) / (0.05 m / ((600 m/s + 200 m/s) / 2))

Finally, we can calculate the force:

F = mass * acceleration

5. Calculation of Work (W):

The work done by the bullet is equal to the force exerted by the bullet multiplied by the distance traveled inside the board.

W = F * distance

Substituting the given values:

W = F * 0.05 m

Let's calculate the values step by step.

Calculation:

1. Calculation of Initial Kinetic Energy (KE_initial):

KE_initial = (1/2) * 0.009 kg * (600 m/s)^2

KE_initial = 1.62 J

2. Calculation of Final Kinetic Energy (KE_final):

KE_final = (1/2) * 0.009 kg * (200 m/s)^2

KE_final = 0.18 J

3. Calculation of Change in Kinetic Energy (ΔKE):

ΔKE = KE_final - KE_initial

ΔKE = 0.18 J - 1.62 J

ΔKE = -1.44 J

4. Calculation of Force (F):

Acceleration = (200 m/s - 600 m/s) / (0.05 m / ((600 m/s + 200 m/s) / 2))

Acceleration = -8000 m/s^2

F = mass * acceleration

F = 0.009 kg * -8000 m/s^2

F = -72 N

5. Calculation of Work (W):

W = F * distance

W = -72 N * 0.05 m

W = -3.6 J

Answer:

The change in kinetic energy of the bullet is -1.44 J (negative because the kinetic energy decreases).

The work done by the bullet is -3.6 J (negative because the force and displacement are in opposite directions).

The value of the resistance force is 72 N (opposite in direction to the motion of the bullet).

Please note that the negative sign indicates that the bullet loses kinetic energy and does negative work on the board, which means the board exerts a resistance force on the bullet.