Question

Импульс тела равен 8 кг*м/с, а кинетическая энергия 16Дж. Найти массу и скорость тела.

Answer 1

MV = 8
(mV^2)/2 = 16

V = 4, m = 2

Answer 2

Calculation of Mass and Velocity

To find the mass and velocity of the body, we can use the formulas for impulse and kinetic energy.

The impulse of a body is equal to the change in momentum, which can be calculated using the formula:

Impulse = Mass × Change in Velocity

The kinetic energy of a body is given by the formula:

Kinetic Energy = 0.5 × Mass × Velocity^2

Given that the impulse of the body is 8 kg·m/s and the kinetic energy is 16 J, we can set up the following equations:

8 = Mass × Change in Velocity (Equation 1)

16 = 0.5 × Mass × Velocity^2 (Equation 2)

To solve for the mass and velocity, we need to eliminate the change in velocity. We can do this by rearranging Equation 1 to solve for the change in velocity:

Change in Velocity = 8 / Mass (Equation 3)

Substituting Equation 3 into Equation 2, we get:

16 = 0.5 × Mass × (8 / Mass)^2

Simplifying the equation further:

16 = 0.5 × Mass × (64 / Mass^2)

16 = 32 / Mass

Solving for the mass:

Mass = 32 / 16 = 2 kg

Now, substituting the mass back into Equation 3 to find the change in velocity:

Change in Velocity = 8 / 2 = 4 m/s

Therefore, the mass of the body is 2 kg and the velocity is 4 m/s.