Question

Тело с массой 2кг имеет импульс p=8i+6j. Какова будет кинетическая энергия в Дж?

Answer 1

Ответ:

4 Дж

Объяснение:

ПРЕДУПРЕЖДАЮ, ВОЗМОЖНО НЕВЕРНО!!!!!!

E к.= mv²/2

Есть масса, найдем скорость

Импульс - mv+m1v1+... и т.д

E к. = 2*2²/2 = 4 Дж

Answer 2

Calculation of Kinetic Energy

To calculate the kinetic energy of an object, we can use the formula:

Kinetic Energy (K.E.) = (1/2) * mass * velocity^2

Given that the mass of the object is 2 kg and the momentum is given as p = 8i + 6j, we need to find the velocity to calculate the kinetic energy.

Finding Velocity from Momentum

The momentum of an object is given by the product of its mass and velocity:

Momentum (p) = mass * velocity

In this case, the momentum is given as p = 8i + 6j, where i and j are the unit vectors in the x and y directions, respectively. We can equate the components of momentum to find the velocity components.

From the given information, we have: - p = 8i + 6j - mass = 2 kg

Equating the x-component of momentum: 8 = mass * velocity_x 8 = 2 * velocity_x velocity_x = 4 m/s

Equating the y-component of momentum: 6 = mass * velocity_y 6 = 2 * velocity_y velocity_y = 3 m/s

Therefore, the velocity of the object is v = 4i + 3j.

Calculation of Kinetic Energy

Now that we have the velocity of the object, we can calculate the kinetic energy using the formula mentioned earlier.

Kinetic Energy (K.E.) = (1/2) * mass * velocity^2

Substituting the values: mass = 2 kg velocity = 4i + 3j

K.E. = (1/2) * 2 * (4i + 3j)^2

Expanding the square: K.E. = (1/2) * 2 * (16i^2 + 24ij + 9j^2)

Simplifying: K.E. = 16i^2 + 24ij + 9j^2

Since i^2 = 1 and j^2 = 1, we can simplify further: K.E. = 16 + 24ij + 9

Finally, we get: K.E. = 25 + 24ij

Therefore, the kinetic energy of the object is 25 + 24ij Joules.

Please note that the answer is in complex form due to the presence of the imaginary unit 'i' in the velocity components.