Question

Задача 4.Камень на высоте 4 м имеет потенциальную энергию 120 Дж.Какова масса камня?Камень падает свободно.Какова кинетическая энергия и скорость камня в момент удара о землю (ч = 0)?

Answer 1

Ответ:

m=3кг,V≈9м/с,Ек=121,5Дж

Объяснение:

Дано:

h=4м

Еп=120Дж

Найти:m,Ек,V

m=Еп/gh

m=120/10*4

m=3кг

V=√2gh

V=√2*10*4

V=√80

V≈9м/с

Ек=mV²/2

Ek=3*9²/2

Ek=121,5Дж

Answer 2

Task 4: Finding the Mass, Kinetic Energy, and Velocity of a Falling Stone

To find the mass of the stone, we can use the formula for potential energy:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Given that the potential energy of the stone is 120 J and the height is 4 m, we can rearrange the formula to solve for the mass:

m = PE / (g * h)

The gravitational acceleration (g) is approximately 9.8 m/s^2.

Let's calculate the mass of the stone:

m = 120 J / (9.8 m/s^2 * 4 m)

Using a calculator, we find that the mass of the stone is approximately 3.06 kg.

Now, let's calculate the kinetic energy and velocity of the stone at the moment of impact with the ground (assuming no air resistance).

The formula for kinetic energy is:

Kinetic Energy (KE) = 0.5 * mass (m) * velocity^2

Since the stone falls freely, we can use the conservation of energy to equate the potential energy at the top to the kinetic energy at the bottom:

Potential Energy (PE) = Kinetic Energy (KE)

Substituting the values we know:

120 J = 0.5 * 3.06 kg * velocity^2

Simplifying the equation:

velocity^2 = (2 * 120 J) / 3.06 kg

Taking the square root of both sides, we can find the velocity:

velocity = sqrt((2 * 120 J) / 3.06 kg)

Using a calculator, we find that the velocity of the stone at the moment of impact is approximately 8 m/s.

Therefore, the mass of the stone is approximately 3.06 kg, and its velocity at the moment of impact is approximately 8 m/s.