Question

HELP! Камень массы m=0.1 кг бросили с поверхности Земли под углом β=30° к горизонту с начальной скоростью v(нулевое)=10 м/с. Пренебрегая сопротивлением воздуха, найти мощность силы тяжести через t=1,5 с после начала движения

Answer 1

Полное время полета t = 2*v₀*sin β / g
t = 2 * 10 м/с * 0,5 / 10 м/с² = 1 с
1 с < 1,5 с тело уже лежит на земле!
Работа силы тяжести будет равна нулю, она не зависит от формы траектории.
Равна нулю будет и мощность.

Answer 2

To find the power of the force of gravity acting on a stone thrown from the surface of the Earth, we need to calculate the work done by gravity over a given time interval. The power is then defined as the rate at which work is done.

Given information:

- Mass of the stone, m = 0.1 kg - Angle of projection, β = 30° - Initial velocity, v₀ = 10 m/s - Time after the start of motion, t = 1.5 s

Calculating the horizontal and vertical components of velocity:

The initial velocity can be resolved into horizontal and vertical components using trigonometry. The horizontal component remains constant throughout the motion, while the vertical component changes due to the acceleration of gravity.

The horizontal component of velocity, v₀x, remains constant and is given by: v₀x = v₀ * cos(β)

The vertical component of velocity, v₀y, changes due to the acceleration of gravity and can be calculated using: v₀y = v₀ * sin(β)

Calculating the displacement in the horizontal direction:

Since there is no acceleration in the horizontal direction, the displacement in the horizontal direction can be calculated using: x = v₀x * t

Calculating the displacement in the vertical direction:

The displacement in the vertical direction can be calculated using the equation of motion: y = v₀y * t + (1/2) * g * t²

Where g is the acceleration due to gravity, which is approximately 9.8 m/s².

Calculating the work done by gravity:

The work done by gravity can be calculated as the product of the force of gravity and the displacement in the vertical direction. The force of gravity is given by: F = m * g

The work done by gravity is then given by: W = F * y

Calculating the power:

The power is defined as the rate at which work is done. It can be calculated by dividing the work done by the time interval: P = W / t

Now, let's calculate the power of the force of gravity acting on the stone.

Calculation:

1. Calculate the horizontal component of velocity: - v₀x = 10 m/s * cos(30°) = 8.66 m/s

2. Calculate the vertical component of velocity: - v₀y = 10 m/s * sin(30°) = 5 m/s

3. Calculate the displacement in the horizontal direction: - x = 8.66 m/s * 1.5 s = 12.99 m

4. Calculate the displacement in the vertical direction: - y = 5 m/s * 1.5 s + (1/2) * 9.8 m/s² * (1.5 s)² = 11.025 m

5. Calculate the force of gravity: - F = 0.1 kg * 9.8 m/s² = 0.98 N

6. Calculate the work done by gravity: - W = 0.98 N * 11.025 m = 10.7735 J

7. Calculate the power: - P = 10.7735 J / 1.5 s = 7.1823 W

Therefore, the power of the force of gravity acting on the stone after 1.5 seconds of motion is approximately 7.1823 watts.