A piston having a diameter of 13.92 cm and a length of 24.13 cm slides downward with a velocity, v through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 0.005cm and the cylinder weighs 0.23kg. Estimate the velocity, v if the oil viscosity is 0.7666 N.s/m2. Assume the velocity distribution in the gap is linear.

Question 2

For an atmospheric pressure of 101 kPa (abs) determine the heights of the fluid columns in barometers containing one of the following liquids a) mercury, b) water, c) ethyl alcohol. Calculate the heights including the effect of vapour pressure and compare the results with those obtained neglecting vapour pressure. Do these results support the widespread use of a particular fluid for barometers? Explain the reason.

Question 3

a) Assume that the purpose of an on-ramp is to allow cars to accelerate from 25 km/h to 100 km/h. An off-ramp will allow cars to decelerate from 100 km/h to 25 km/h. Should an off-ramp be longer than, shorter than or the same length as an on-ramp? Give a reason for your answer.

b) Suppose you were going to accelerate a 2000 kg car by the Rube Goldberg contraption shown in Figure. The fan (A) blows apples (C) off the tree (B) into the funnel and thus into the bag (D). The bag is pulled downward by the force of gravity (equal to the weight of the apples in the bag), and that force is transmitted via the pulley (E) to accelerate the car (F). About how many apples each weighing 1.00 N would have to fall into the bag in order to achieve 0 to 26.82 m/s in 7.00 seconds? Assume the filled bag applies a constant force to the car equal to the weight of the apples in the bag.