Dentist

A doctor lifts a chair with a patient using a hydraulic device. The area of the smaller piston is 5 cm². The area of the larger piston is 200 cm². The mass of the chair is 30 kg, the mass of the patient 100 kg. Will the doctor lift the chair with the patient to a suitable height for his work with a force of 20 N if he acts on the smaller piston with this force? (If the force of 20 N will not suffice to lift the chair with the patient, the device must be suitably modified. The area of the smaller piston remains the same)

Final Answer:

F =  32.5 N

Step-by-step explanation:

$$\begin{gathered} S_1=5{\text{cm}}^2 \\ {S}_2=200{\text{cm}}^2 \\ g=10{\text{m/s}}^2 \\ m=30+100=130\text{kg} \\ {F}_1=20\text{N} \\ {F}_2=m\cdot g=130\cdot 10=1300\text{N} \\ {p}_1=p_2 \\ {F}_1/S_1=F_2/S_2 \\ F{S}_2=F_2{S}_1 \\ F=F_2\cdot \frac{S_1}{S_2}=1300\cdot \frac{5}{200}=\frac{1300\cdot 5}{200}=\frac{6500}{200}=\frac{65}{2}=32.5=\frac{65}{2}\text{N}=32.5\text{N} \\ F>F_1 \end{gathered}$$

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