Question

A barber raises his customer’s chair by applying a force of 100 N to a hydraulic piston of area 0.01 m2. If the chair is attached to a piston of area 0.1 m2, how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg. ​

Answer 1

Парикмахер поднимает стул своего клиента, прикладывая усилие в 100 н к гидравлическому поршню площадью 0,01 м2. Если кресло крепится к поршню площадью 0,1 м2, то насколько массивным может быть клиент? Предположим, что само кресло имеет массу 5 кг.

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Соотношение сил и площадей в гидравлическом прессе:

(The ratio of forces and areas in a hydraulic press:)

         F₁/S₁ = F₂/S₂

Тогда усилие, развиваемое на большом поршне:

(Then the force generated on the large piston:)

         F₂ = F₁S₂/S₁ = 100 · 0,1 : 0,01 = 1000 (Н)

Вес кресла (The weight of the chair):

         Р = mg = 5 · 10 = 50 (H)

Максимально возможный вес клиента при усилии на малом поршне 100 Н (The maximum possible weight of the customer with a force on a small piston is 100 N):

         P' = F₂ - P = 1000 - 50 = 950 (H)

Масса клиента (Сustomer mass):

         m = P'/g = 950 : 10 = 95 (кг)

Answer 2

To solve this problem, we can use Pascal's law, which states that pressure exerted on a fluid is transmitted uniformly in all directions. Based on this principle, we can calculate the force exerted by the hydraulic piston on the chair.

First, let's calculate the pressure exerted by the barber's force on the hydraulic piston. The formula for pressure is:

Pressure = Force / Area

Therefore, the pressure exerted by the barber's force is:

Pressure = 100 N / 0.01 m^2 = 10,000 Pa

Now, since the pressure is transmitted uniformly, the pressure on the customer's chair will also be 10,000 Pa.

Next, we can calculate the force exerted by the customer's chair using the formula:

Force = Pressure * Area

The area of the customer's chair piston is 0.1 m^2. Therefore, the force exerted by the chair is:

Force = 10,000 Pa * 0.1 m^2 = 1,000 N

Finally, we need to consider the weight of the chair itself. The weight of an object is given by the formula:

Weight = mass * gravitational acceleration

The mass of the chair is 5 kg, and the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight of the chair is:

Weight = 5 kg * 9.8 m/s^2 = 49 N

To determine the maximum mass of a customer the chair can raise, we subtract the weight of the chair from the force exerted by the chair:

Maximum Mass = (Force - Weight) / gravitational acceleration

Maximum Mass = (1,000 N - 49 N) / 9.8 m/s^2 ≈ 95.92 kg

Therefore, the chair can raise a customer with a mass of approximately 95.92 kg.