Question

Груз полностью погруженный в жидкость,висит неподвижно на упругой пружине.будет ли в этом случае модуль силы тяжести равен сумме модулей силы упругости и выталкивающей силы?ответ обоснуйте.

Answer 1

Да!
Так как ускорение у груза равно нулю (висит неподвижно), то по закону Ньютона F=ma;
F=m*0; => F=0.
Следовательно равнодействующая всех сил равна нулю.
Fт+Fа+Fу=0; (это векторы!!!)
Силы Архимеда и упругости направлены в одну сторону, а сила тяжести в противоположную, значит их знаки различны. Пусть направление "вниз" будет положительным, тогда получим для модулей сил:
Fт-Fа-Fу=0;
Fт=Fа+Fу;

Answer 2

Analysis of the Situation

When a mass is fully immersed in a liquid and is suspended by a spring, several forces are at play. These include the force of gravity acting on the mass, the force of buoyancy exerted by the liquid, and the force of the spring pushing upwards. The question asks whether in this scenario, the magnitude of the force of gravity is equal to the sum of the magnitudes of the spring force and the buoyant force.

Answer

In this case, the module of the force of gravity is not equal to the sum of the modules of the force of elasticity and the force of buoyancy. The force of gravity is balanced by the sum of the force of elasticity and the force of buoyancy, which is why the mass is suspended in equilibrium.

The force of gravity is given by the mass of the object multiplied by the acceleration due to gravity, while the force of elasticity is determined by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The force of buoyancy, on the other hand, is equal to the weight of the liquid displaced by the object.

Explanation

The force of gravity, denoted as F_g, is given by the equation: F_g = mg Where: - m is the mass of the object - g is the acceleration due to gravity

The force of elasticity, denoted as F_e, is given by Hooke's Law: F_e = -kx Where: - k is the spring constant - x is the displacement from the equilibrium position

The force of buoyancy, denoted as F_b, is equal to the weight of the liquid displaced by the object, which is given by Archimedes' principle: F_b = ρVg Where: - ρ is the density of the liquid - V is the volume of the liquid displaced - g is the acceleration due to gravity

In equilibrium, the sum of the forces is zero: ΣF = F_g + F_e + F_b = 0

Therefore, the force of gravity is balanced by the sum of the force of elasticity and the force of buoyancy, but it is not necessarily equal to their sum.