A screw jack with a Tommy bar of length 12cm is used to raise a car through a vertical height of 25cm by turning the Tommy bar through 50 revolutions. Calcu...

A screw jack with a Tommy bar of length 12cm is used to raise a car through a vertical height of 25cm by turning the Tommy bar through 50 revolutions. Calculate the approximate velocity ratio of the jack [\(\pi = 3.142\)]

Answer Details

A screw jack is a simple machine used to lift heavy loads with little effort. The velocity ratio of a screw jack is defined as the ratio of the distance moved by the effort (Tommy bar) to the distance moved by the load (car). In this case, the car is raised through a vertical height of 25cm by turning the Tommy bar through 50 revolutions. The distance moved by the effort is the circumference of the circle traced out by the end of the Tommy bar, which is given by: circumference = 2πr = 2 x 3.142 x 0.12m = 0.754m (approx.) Since the Tommy bar is turned through 50 revolutions, the total distance moved by the effort is: distance moved by effort = 0.754m x 50 = 37.7m (approx.) Therefore, the velocity ratio is: velocity ratio = distance moved by effort / distance moved by load = 37.7m / 0.25m = 150.8 (approx.) So the approximate velocity ratio of the jack is 151, which is closest to.