Question

Как во сколько раз изменится кинетическая энергия тела,если его масса уменьшится в 5 раз, а скорость увеличится в 3 раза?

Answer 1

Eк1=m1*U1^2/2
Eк2=m2*U2^2/2=(m1/5)*U1^2*9/2, т.е увеличится в 9/5 =1.8 раз

Answer 2

Calculation of Change in Kinetic Energy

To calculate the change in kinetic energy of an object, we need to consider both its mass and velocity. In this case, the mass of the object decreases by a factor of 5, while the velocity increases by a factor of 3.

The formula for kinetic energy is given by:

Kinetic Energy (Ek) = (1/2) * mass * velocity^2 Let's denote the initial mass as m0, the final mass as mf, the initial velocity as v0, and the final velocity as vf.

Given that the mass decreases by a factor of 5 (mf = m0/5) and the velocity increases by a factor of 3 (vf = 3 * v0), we can calculate the change in kinetic energy.

The initial kinetic energy (Ek0) is given by:

Ek0 = (1/2) * m0 * v0^2

The final kinetic energy (Ekf) is given by:

Ekf = (1/2) * mf * vf^2 = (1/2) * (m0/5) * (3 * v0)^2 = (1/2) * (m0/5) * 9 * v0^2 = (9/10) * m0 * v0^2

The change in kinetic energy (ΔEk) is given by:

ΔEk = Ekf - Ek0 = (9/10) * m0 * v0^2 - (1/2) * m0 * v0^2 = (9/10 - 1/2) * m0 * v0^2 = (9/10 - 5/10) * m0 * v0^2 = (4/10) * m0 * v0^2 = (2/5) * m0 * v0^2

Therefore, the change in kinetic energy is equal to (2/5) * m0 * v0^2.

Please note that this calculation assumes that the object is moving in a straight line and that there are no external forces acting on it.

Let me know if there's anything else I can help you with!