A dentist\'s chair with a patient in it weighs 2120 N. The output plunger of a h

Question

A dentist's chair with a patient in it weighs 2120 N. The output plunger of a hydraulic system begins to lift the chair when the dentist's foot applies a force of 54 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston? A dump truck uses a hydraulic cylinder, as the drawing illustrates. When activated by the operator, a pump injects hydraulic oil into the cylinder at an absolute pressure of 3.52 times 10^6 Pa and drives the output plunger, which has a radius of 0.163 m. Assuming that the plunger remains perpendicular to the floor of the load bed, find the torque that the plunger creates about the axis identified in the drawing. A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3516 N/m. The piston has a negligible mass and a radius of 0.015 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?

Explanation / Answer

pressure at the plunger = pressure at the piston

F1*A1 = F2*A2

F1*pi*r1^2 = F2*pi*r2^2

r1/r2 = sqrt(F2/F1)

r1/r2 = sqrt(54/2120)

r1/r2 = 0.16 <<<------answer

++++++++++++++++++++

force F = P*A

torque = force *perpendicular distance

torque = 3.52*10^6*pi*0.163^2*3.5

torque = 1028337.8 Nm

+++++++++++++++

(a)

In equilibrium

F = k*x

P*A = k*x

1.013*10^5*pi*0.015^2 = 3516*x

x = 0.02 m

(b)

work = 0.5*k*x^2 = 0.5*3516*0.02^2 = 0.7032 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.