Question

Please show and explain all of the steps.

A steel beam 13 m long (at 20°C) is jutted next to a concert wall. If the temperature can increase to 45°C, what should be the minimum amount of gap left between wall and block? What I've done: ΔT: 45°C – 20°C = 25°C    Formula: ΔL = αL_o • ΔT

A dentist chair makes use of hydraulics. The chair and the patient exert a downward force of 2300 N. The chair is attached to a large piston with an area of 1200 cm³. To move the chair a pump applies a force to a small piston with an area of 88 cm³. What force must be excreted to lift the chair? I know its Pascals Principal: P₁ = P₂

Answer 1

Both the answers are given in the figure.

a) Here the answer is 2.34mm. If this doesn't match with the original answer just consider the expansion of concrete which has an expansion coefficient of about 10^-7.

b) Here the answer is 168.67 N. As per the Pascal's law the pressure is transferred equally in the fluid and hence a small force applied on a small area will get magnified at a larger area so that the force to area ratio(which is pressure) remains same.