Question

Кинетическая энергия тела, падающего с высоты 2.4 м, в определённый момент становиться в 3 раза больше потенциальной. Определите скорость тела и высоту, на которой это произошло.

Answer 1

По условию Ек₁=3Ер₁
по закону сохранения энергии Ек₁+Ер₁=Е=mgh (полная энергия в верхней точке)
3Ер₁+Ер₁=mgh
4Ер₁=mgh
4mgh₁=mgh
h₁=h/4=2,4/4=0,6м
Ek₁=mv₁²/2=3mgh₁ отсюда находим квадрат скорости
v₁²=6gh
v₁=√6gh=√6*10*0,6=√36= 6м/с

Answer 2

Kinetic and Potential Energy of a Falling Object

When an object falls from a height, its potential energy is converted into kinetic energy as it gains speed. The relationship between the kinetic energy (KE) and potential energy (PE) of a falling object can be expressed as:

KE = 3 * PE We are given that the kinetic energy of the object at a certain moment is three times greater than its potential energy. We need to determine the velocity of the object and the height at which this occurs.

Solution:

Let's assume the mass of the object is m.

The potential energy of the object at a height of 2.4 m can be calculated using the formula:

PE = m * g * h where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height (2.4 m).

Substituting the given values, we have:

PE = m * 9.8 * 2.4

The kinetic energy of the object can be calculated using the formula:

KE = (1/2) * m * v^2 where v is the velocity of the object.

Since we know that KE = 3 * PE, we can equate the two equations:

(1/2) * m * v^2 = 3 * m * 9.8 * 2.4

Simplifying the equation, we get:

v^2 = 3 * 9.8 * 2.4 * 2

Taking the square root of both sides, we find:

v = sqrt(3 * 9.8 * 2.4 * 2)

Now, let's calculate the velocity:

v ≈ 9.8 m/s The velocity of the object is approximately 9.8 m/s.

To find the height at which this occurs, we can use the equation for potential energy:

PE = m * g * h

Rearranging the equation to solve for h, we have:

h = PE / (m * g)

Substituting the known values, we get:

h = (3 * m * 9.8 * 2.4) / (m * 9.8)

Simplifying the equation, we find:

h = 3 * 2.4

Now, let's calculate the height:

h = 7.2 m The height at which the kinetic energy of the object becomes three times greater than its potential energy is approximately 7.2 m.

Therefore, the velocity of the object at this height is approximately 9.8 m/s, and the height is approximately 7.2 m.

Please note that the above calculations assume no air resistance and a constant gravitational acceleration.