Question

Стальную деталь объёмом 0,4 м3 и плотностью 7800 кг/м3 поднимают равномерно и на высоту 15 метров за 30 секунд. Найти: а) массу тела; б) силу тяжести, действующую на тело; в) вес тела; г) работу по подъёму тела; д) развиваемую при этом мощность; е) скорость подъёма; ж) импульс тела; з) потонцеальную энергию в верхней точке; и) кинетическую энергию при подъеме; к)* выталкивающую силу при погружении ( плотность керосина 800 кг/м3 ); л)* вес тела в керосине.

Answer 1

Given Information:

- Volume of the steel object: 0.4 m^3 - Density of the steel: 7800 kg/m^3 - Height lifted: 15 meters - Time taken to lift: 30 seconds - Density of kerosene: 800 kg/m^3

Calculations and Results:

a) Mass of the object: The mass of an object can be calculated using the formula: mass = density * volume. Given that the volume is 0.4 m^3 and the density is 7800 kg/m^3, we can calculate the mass as follows: mass = 7800 kg/m^3 * 0.4 m^3 = 3120 kg.

b) Force of gravity on the object: The force of gravity acting on an object can be calculated using the formula: force = mass * acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the force of gravity on the object is: force = 3120 kg * 9.8 m/s^2 = 30576 N.

c) Weight of the object: The weight of an object is the force of gravity acting on it. Therefore, the weight of the object is also 30576 N.

d) Work done in lifting the object: The work done in lifting an object can be calculated using the formula: work = force * distance. Given that the force is 30576 N and the distance is 15 meters, we can calculate the work as follows: work = 30576 N * 15 m = 458,640 J (joules).

e) Power developed in lifting the object: The power developed in lifting an object can be calculated using the formula: power = work / time. Given that the work is 458,640 J and the time is 30 seconds, we can calculate the power as follows: power = 458,640 J / 30 s = 15,288 W (watts).

f) Speed of lifting: The speed of lifting can be calculated using the formula: speed = distance / time. Given that the distance is 15 meters and the time is 30 seconds, we can calculate the speed as follows: speed = 15 m / 30 s = 0.5 m/s.

g) Impulse of the object: The impulse of an object can be calculated using the formula: impulse = force * time. Given that the force is 30576 N and the time is 30 seconds, we can calculate the impulse as follows: impulse = 30576 N * 30 s = 917,280 Ns (newton-seconds).

h) Potential energy at the top: The potential energy of an object at a certain height can be calculated using the formula: potential energy = mass * acceleration due to gravity * height. Given that the mass is 3120 kg, the acceleration due to gravity is 9.8 m/s^2, and the height is 15 meters, we can calculate the potential energy as follows: potential energy = 3120 kg * 9.8 m/s^2 * 15 m = 458,640 J (joules).

i) Kinetic energy during lifting: The kinetic energy of an object during lifting can be calculated using the formula: kinetic energy = 0.5 * mass * velocity^2. Given that the mass is 3120 kg and the velocity is 0.5 m/s, we can calculate the kinetic energy as follows: kinetic energy = 0.5 * 3120 kg * (0.5 m/s)^2 = 195 J (joules).

k) Buoyant force during submersion in kerosene: The buoyant force experienced by an object submerged in a fluid can be calculated using the formula: buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity. Given that the density of kerosene is 800 kg/m^3 and the volume of the object is 0.4 m^3, we can calculate the buoyant force as follows: buoyant force = 800 kg/m^3 * 0.4 m^3 * 9.8 m/s^2 = 3136 N.

l) Weight of the object in kerosene: The weight of an object in a fluid can be calculated using the formula: weight in fluid = weight in air - buoyant force. Given that the weight in air is 30576 N and the buoyant force is 3136 N, we can calculate the weight of the object in kerosene as follows: weight in kerosene = 30576 N - 3136 N = 27440 N.

Summary of Results: a) Mass of the object: 3120 kg b) Force of gravity on the object: 30576 N c) Weight of the object: 30576 N d) Work done in lifting the object: 458,640 J e) Power developed in lifting the object: 15,288 W f) Speed of lifting: 0.5 m/s g) Impulse of the object: 917,280 Ns h) Potential energy at the top: 458,640 J i) Kinetic energy during lifting: 195 J k) Buoyant force during submersion in kerosene: 3136 N l) Weight of the object in kerosene: 27440 N

Please note that the calculations above assume ideal conditions and do not take into account factors such as air resistance or friction.