Moments, Pressure & Hooke's Law

Science · Forces & Motion · ages 12-14

Name ______________________ Date ____________

You double the force on a piston while keeping its area fixed. What happens to the pressure added by the piston?
- It doubles
- It halves
- It stays the same
Pascal's principle means total pressure must be equal at the top and bottom of a tall closed container of water.
Circle one: True False
A 10 N force acts along a straight lever. Its line of action passes through the pivot. What is its moment, in Nm?
Answer: ______________
Only two forces create moments on a lever: 12 N with a perpendicular distance of 0.5 m acts clockwise; 8 N with a perpendicular distance of 0.25 m acts anticlockwise. Find the net clockwise moment, in Nm.
Answer: ______________
An ideal hydraulic lift has pistons at the same height. Why does the larger output piston produce more force?
- The same pressure acts over a larger area
- The larger piston makes the liquid gain weight
- The pipe's friction adds force to the output
Two perpendicular pushes on a door both turn it clockwise: 18 N at 0.4 m from the hinge and 10 N at 0.3 m. What is their combined clockwise moment, in Nm?
Answer: ______________
Two points on a spring's straight proportional force-extension graph are (0.01 m, 3 N) and (0.03 m, 9 N). Find its slope k, in N/m.
Answer: ______________
Spring A has k = 5 N/cm and spring B has k = 10 N/cm. Both obey Hooke's Law under the same force. Which extends less?
- Spring B: a larger k gives less extension
- Spring A: a smaller k gives less extension
- Neither: equal force gives equal extension
If both force and perpendicular distance from the pivot to its line of action double, the moment doubles.
Circle one: True False
A spring's force-extension graph is straight through the origin up to 8 N, then curves. What does the curve show?
- The spring must already be permanently stretched
- Force and extension are no longer proportional
- The spring now extends without any applied force

Answer key

For grown-ups. Fold this page away before handing over the rest.

Moments, Pressure & Hooke's Law W1-mt_vuNjYx3qOy-s1

It doubles · Pressure = force ÷ area. With the same area, doubling the force doubles the added pressure.
False · The added pressure is transmitted unchanged. Total pressure can still differ with depth.
0 · The perpendicular distance is zero, so moment = 10 × 0 = 0 Nm.
4 · Clockwise moment is 6 Nm; anticlockwise moment is 2 Nm. The net is 6 - 2 = 4 Nm clockwise.
The same pressure acts over a larger area · Force = pressure × area. At the same pressure, the larger piston area gives the larger force.
10.2 · The moments act the same way, so add: 18 × 0.4 + 10 × 0.3 = 7.2 + 3 = 10.2 Nm.
300 · k = change in force ÷ change in extension = (9 - 3) ÷ (0.03 - 0.01) = 6 ÷ 0.02 = 300 N/m.
Spring B: a larger k gives less extension · Extension = force ÷ k. With the same force, dividing by B's larger k gives less extension.
False · Moment = force × perpendicular distance. Doubling both gives 2 × 2 = 4 times the moment.
Force and extension are no longer proportional · The curve shows the spring has passed its limit of proportionality. Unloading is needed to test for permanent extension.