S3U

Science / Forces / Grade 7 / sf760

Hydraulic Press: Square the Diameter Ratio

Distinguish diameter ratios from area ratios.

All worksheets
5 questions0m 0s
Learn the skill

For circular faces A = pi d^2 / 4. For two faces, the common factors cancel: area ratio = (output diameter / input diameter)^2. Use an ideal press with equal-height faces and negligible friction. Use diagrams and calculations only; never build or operate a press for this activity.

Worked example

Diameters of 2 cm and 6 cm give a diameter ratio of 3 and an area ratio of 9. A 7 N input gives 63 N, not 21 N.

Circular input diameter is 2 centimeters and output diameter is 6 centimeters. The output diameter is three times as large and its area is nine times as large.
Circular input diameter is 2 centimeters and output diameter is 6 centimeters. The output diameter is three times as large and its area is nine times as large.
Question 1 For diameters 2 cm and 6 cm, what is the diameter ratio?
Question 2 What is the corresponding area ratio?
Question 3 What output force follows from a 7 N input?
Question 4 For 9 cm input travel, what is the ideal output travel?
Question 5 If both diameters double, what happens to their area ratio?