The Problem

(1)

The time T needed to mill a channel varies directly as the length, width, and depth of the channel, assuming the cutting tool and material being machined stay constant.

a) Write this as an equation using a constant of proportionality;

b) A channel 30 cm long, 5.0cm wide and 4.5 cm deep took 36 minutes to mill. Use this information to determine the constant proportionality,with units.

c) How long will it take to mill a channel in the same material, 45 cm long, 6.4 cm wide, and 3.75 cm deep?

d) How long would the machining job ofb)above take, if the length, width, and depth werealldoubled

(2)It takes three men three hours to assemble three shelving units. How long will it take nine men to assemble twelve shelving units?Prove your answer

(3)The time taken to machine out the interior of a hollow cylinder in a shaft on a lathe varies directly as the length of the cylinder and directly as the square of the internal diameter.

a) Write this as an equation using a constant of proportionality;

b) It took 22 minutes to machine out a cylinder 14.5 cm long and 3.45 cm in diameter. Use this information to determine the constant of proportionality,with units.

c) How long would it take to machine out a cylinder 9.6 cm long, and 5.90 cm in diameter?

(4)The cutting speed of a milling cutter varies directly as the diameter of the cutteranddirectly as the RPM of the cutter.

a) Write this as an equation using a constant of proportionality;

b) Turing a milling cutter 8.5 cm in diamter at 6250 RPM results in a cutting speed of 2.78 m/s. Use this information to determine the constant of proportionality,with units.

c) Calculate the needed RPM to produce a recommended cutting speed of 4.25 m/s (in another material), using a 12.5 diameter cutter.