Question

Тело массой 2кг падает с высоты 10 м вертикально вниз без начальной скорости. Найти: время падения, полную механическую энергию тела. максимальную кинетическую энергию тела

Answer 1

Скорость тела изменяется по закону v=-g*t, а  высота - по закону h=h0-g*t*t/2, где ho=10 м. Решая уравнение 10-4,905*t*t=0, находим t=1,43c.
Скорость максимальна в момент приземления, её величина по модулю составит 9,81*1,43=14 м/с, а кинетическая энергия E=m*v*v/2 = 196 Дж. Потенциальная энергия максимальна в начальный момент и составляет m*g*h=196, т.е. согласно закону сохранения энергии равна максимальной кинетической. При падении первая убывает, а вторая возрастает, но их сумма - полная энергия - остаётся постоянной и равной 196 Дж.

Answer 2

Calculation of Time of Fall

To calculate the time of fall for an object with a mass of 2 kg falling vertically from a height of 10 m without any initial velocity, we can use the equation:

h = (1/2)gt^2

where: - h is the height (10 m) - g is the acceleration due to gravity (9.8 m/s^2) - t is the time of fall (unknown)

Rearranging the equation, we get:

t = sqrt(2h/g)

Substituting the given values, we can calculate the time of fall:

t = sqrt(2 * 10 / 9.8) ≈ 1.43 seconds.

Therefore, the time of fall is approximately 1.43 seconds.

Calculation of Total Mechanical Energy

The total mechanical energy of an object is the sum of its potential energy and kinetic energy. In this case, since the object starts from rest at a height of 10 m, the initial kinetic energy is zero.

The potential energy of the object at the starting height can be calculated using the equation:

PE = mgh

where: - PE is the potential energy - m is the mass of the object (2 kg) - g is the acceleration due to gravity (9.8 m/s^2) - h is the height (10 m)

Substituting the given values, we can calculate the potential energy:

PE = 2 * 9.8 * 10 = 196 J.

Therefore, the total mechanical energy of the object is 196 J.

Calculation of Maximum Kinetic Energy

The maximum kinetic energy of the object occurs at the lowest point of its fall, where its potential energy is zero. At this point, all of the potential energy is converted into kinetic energy.

The maximum kinetic energy can be calculated using the equation:

KE = (1/2)mv^2

where: - KE is the kinetic energy - m is the mass of the object (2 kg) - v is the velocity at the lowest point (unknown)

Since the object falls vertically without any initial velocity, the velocity at the lowest point can be calculated using the equation:

v = gt

Substituting the value of g (9.8 m/s^2) and the time of fall (1.43 seconds), we can calculate the velocity at the lowest point:

v = 9.8 * 1.43 ≈ 14.014 m/s.

Now, substituting the calculated velocity into the equation for kinetic energy, we can calculate the maximum kinetic energy:

KE = (1/2) * 2 * (14.014)^2 ≈ 392.3 J.

Therefore, the maximum kinetic energy of the object is approximately 392.3 J.