Question

Тело массой 0.5 кг брошено вертикально вверх со скоростью 4 м/с. Найдите работу силы тяжести , изменение потенциальной энергии и кинетической энергии при подъеме тела до максимальной высоты.

Answer 1

Работа силы тяжести (A) будет равна (-m*g*h), тк она направлена против движения тела.

Конечная скорость тела=начальная скорость - ускорение своб.пад. * время

Время до верхней точки равно 0,4с.

$h=V_{0}t - \frac{gt^{2}}{2}$ 

Высота подъема тела равно 0,8м

Тогда работа равна    A=-0,5*10*0,8=-4Дж 

 

Answer 2

Calculation of Work Done by Gravity

To calculate the work done by gravity when the body is lifted to its maximum height, we need to consider the change in potential energy. The work done by gravity is equal to the change in potential energy.

The formula for calculating the work done by gravity is:

Work done by gravity = Change in potential energy

The potential energy of an object at a certain height is given by the formula:

Potential energy = mass * acceleration due to gravity * height

Given: - Mass of the body (m) = 0.5 kg - Initial velocity (u) = 4 m/s (upwards) - Final velocity (v) = 0 m/s (at maximum height)

To find the change in potential energy, we need to calculate the height to which the body is lifted.

Using the equation of motion:

v^2 = u^2 + 2as

where: - v = final velocity - u = initial velocity - a = acceleration (acceleration due to gravity) - s = displacement (height)

Rearranging the equation, we get:

s = (v^2 - u^2) / (2a)

Substituting the given values, we can calculate the height (s):

s = (0^2 - 4^2) / (2 * (-9.8))

Calculating the value of s, we find:

s ≈ 0.82 meters

Now, we can calculate the change in potential energy:

Change in potential energy = mass * acceleration due to gravity * height

Substituting the values, we get:

Change in potential energy = 0.5 kg * (-9.8 m/s^2) * 0.82 m

Calculating the value, we find:

Change in potential energy ≈ -4.03 Joules

The negative sign indicates that the potential energy decreases as the body is lifted against gravity.

Calculation of Change in Kinetic Energy

To calculate the change in kinetic energy, we need to consider the initial and final velocities of the body.

The formula for calculating the change in kinetic energy is:

Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)

Given: - Mass of the body (m) = 0.5 kg - Initial velocity (u) = 4 m/s (upwards) - Final velocity (v) = 0 m/s (at maximum height)

Substituting the values, we can calculate the change in kinetic energy:

Change in kinetic energy = (1/2) * 0.5 kg * (0^2 - 4^2)

Calculating the value, we find:

Change in kinetic energy ≈ -8 Joules

The negative sign indicates that the kinetic energy decreases as the body moves upwards against gravity.

Summary of Results

The results of the calculations are as follows:

- Work done by gravity: -4.03 Joules - Change in potential energy: -4.03 Joules - Change in kinetic energy: -8 Joules

Please note that the negative signs indicate a decrease in potential and kinetic energy as the body is lifted against gravity.

I hope this helps! Let me know if you have any further questions.