Question

8.27 Тело массой 2,5 кг падает с высоты 12 м. Чему равна потенциалы ная энергия тела на высоте 12 м? 8 м? Определите скорость тела в момент падения на землю.

Answer 1

Дано:

m = 2.5 кг

h₁ = 12 м

h₂ = 8 м

Найти: E₁, E₂, v

Решение:

Найдем потенциальную энергию тела на высоте 12 метров:

$E_\Pi_1=mgh_1$

$E_\Pi_1=2.5\cdot10\cdot12=300\ \mathrm{(Dg)}$

Эта же энергия представляет собой полную энергию тела:

$E=E_\Pi_1=300\ \mathrm{(Dg)}$

Найдем потенциальную энергию тела на высоте 8 метров:

$E_\Pi_2=mgh_2$

$E_\Pi_2=2.5\cdot10\cdot8=200\ \mathrm{(Dg)}$

Скорость тела в момент падения на землю определим через его кинетическую энергию. В момент падения кинетическая энергия равна полной энергии:

$E=E_K=\dfrac{mv^2}{2}$

$mv^2=2E$

$v^2=\dfrac{2E}{m}$

$v=\sqrt{\dfrac{2E}{m} }$

$v=\sqrt{\dfrac{2\cdot300}{2.5} }=\sqrt{240} \approx15.5\ \mathrm{(m/s)}$

Ответ:

потенциальная энергия тела на высоте 12 метров равна 300 Дж;

потенциальная энергия тела на высоте 8 метров равна 200 Дж;

скорость тела в момент падения приближенно равна 15.5 м/с

Answer 2

Еп=mgh

1) Eп1=2,5*10*12=300 Дж

2) Еп2=2,5*10*8=200 Дж

3) Еп1=Ек

Ек=mV²/2

2Ek=mV²

V²=2Ek/m

V=√(2Ek/m)

V=√(2*300/2,5)=√(100*6/2,5)=10√(2,4)=10√(4*0,6)=20√0,6=20*0,775=

15,5 м/с  -  это ответ.

Answer 3

Calculation of Potential Energy at Different Heights

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

Potential Energy = mass * gravity * height

Given that the mass of the object is 2.5 kg and it falls from a height of 12 m, we can calculate the potential energy at that height:

Potential Energy at 12 m = 2.5 kg * 9.8 m/s^2 * 12 m

Using this formula, we find that the potential energy at a height of 12 m is 294 J.

Similarly, we can calculate the potential energy at a height of 8 m:

Potential Energy at 8 m = 2.5 kg * 9.8 m/s^2 * 8 m

Using this formula, we find that the potential energy at a height of 8 m is 196 J.

Calculation of Velocity at the Moment of Impact

To calculate the velocity of the object at the moment it hits the ground, we can use the principle of conservation of energy. At the moment of impact, all the potential energy is converted into kinetic energy.

The formula for kinetic energy is:

Kinetic Energy = 0.5 * mass * velocity^2

Since all the potential energy is converted into kinetic energy, we can equate the potential energy at 12 m to the kinetic energy at the moment of impact:

Potential Energy at 12 m = Kinetic Energy at impact

Using this equation, we can solve for the velocity at the moment of impact:

Potential Energy at 12 m = 0.5 * mass * velocity^2

294 J = 0.5 * 2.5 kg * velocity^2

Simplifying the equation, we find:

velocity^2 = (2 * 294 J) / (2.5 kg)

velocity^2 = 235.2 J / 2.5 kg

velocity^2 = 94.08 m^2/s^2

Taking the square root of both sides, we find:

velocity = √(94.08 m^2/s^2)

Calculating the square root, we find that the velocity at the moment of impact is approximately 9.7 m/s.

Please note that these calculations assume no air resistance and a constant gravitational acceleration of 9.8 m/s^2.