A bus brakes in a straight line with a steady deceleration of magnitude

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow

Fluids and Continuum Physics, Ch Euler's equation and Bernoulli's theorem

Problem

A bus brakes in a straight line with a steady deceleration of magnitude 2.5 m s−22.5\ \mathrm{m\ s^{-2}}. A passenger holds a cylindrical cup of coffee of inner diameter 7.0 cm7.0\ \mathrm{cm}, held with its axis vertical. Long enough after the braking began, the coffee moves with the bus as a rigid body, so every parcel has the same horizontal acceleration; the coffee is incompressible and inviscid and the air above it is at atmospheric pressure. Take g=9.8 m s−2g = 9.8\ \mathrm{m\ s^{-2}}. ((a)) Find the angle the free surface makes with the horizontal. ((b)) Find the height difference between the two ends of a diameter of the surface taken along the direction of travel.

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