Question

Поршень площадью 10 см2 может без трения перемещаться в верти­кальном цилиндрическом сосуде, обеспечивая при этом его герме­тичность. Сосуд с поршнем, заполненный газом покоится на полу неподвижного лифта при атмосферном давлении 100 кПа, при этом расстоя­ние от нижнего края поршня до дна сосуда находится на расстоянии 20 см. Когда лифт поедет вверх с ускорением равным 4 м/с2, пор­шень сместится на 2,5 см. Какова масса поршня, если изменение температуры газа можно не учитывать?

Answer 1

S=10^-3 м2   p1=10^5 Па   h=0.2 м   a=4 м/с2   Δh=0.025 м     m=?
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p1*V1=p2*V2
p2=m*(g+a)/S + p1
V1=S*h
V2=S*(h-Δh)
p1*h/(h-Δh)=m*(g+a)/S + p1
m=p1*S*(h/(h-Δh) - 1)/(g+a)=10^5*10^-3*(0.2/(0.2-0.025 - 1)/(10+4)≈8.2 кг
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Answer 2

Calculation of the Piston's Mass

To calculate the mass of the piston, we need to consider the forces acting on it and use Newton's second law of motion.

The force acting on the piston is the difference between the atmospheric pressure and the pressure inside the cylinder. Since the piston is in equilibrium, the net force acting on it is zero. Therefore, the force due to the pressure difference is balanced by the force due to the acceleration of the lift.

Let's break down the calculation step by step:

1. Calculate the force due to the pressure difference: - The area of the piston is given as 10 cm². - The pressure inside the cylinder is the same as the atmospheric pressure, which is 100 kPa. - The force due to the pressure difference is given by the formula: force = pressure × area.

2. Calculate the force due to the acceleration of the lift: - The acceleration of the lift is given as 4 m/s². - The mass of the lift is equal to the mass of the piston. - The force due to the acceleration of the lift is given by the formula: force = mass × acceleration.

3. Equate the two forces and solve for the mass of the piston.

Let's perform the calculations:

1. Calculate the force due to the pressure difference: - Area of the piston = 10 cm² = 0.001 m². - Pressure inside the cylinder = atmospheric pressure = 100 kPa = 100,000 Pa. - Force due to the pressure difference = pressure × area.

2. Calculate the force due to the acceleration of the lift: - Acceleration of the lift = 4 m/s². - Force due to the acceleration of the lift = mass × acceleration.

3. Equate the two forces and solve for the mass of the piston.

Please wait a moment while I perform the calculations.