AMME1802 Chap.7 Friction and Flexible Belts
Friction and Flexible Belts
Friction problems are equilibrium problems with an inequality and a direction decision. This chapter distinguishes required static friction from its limiting value, solves normal force before applying a coefficient, and extends impending-slip logic to flexible belts. The final answer always states the contact regime as well as the force magnitude.
Static friction supplies only the amount needed for equilibrium until its bound is reached. The normal force is solved from the full free-body diagram and need not equal weight when a pull, incline or second contact changes it. Impending motion supplies the equality with the static coefficient; sliding uses the kinetic model.
Ladder and wheel problems may have several candidate motions, while belt problems require a wrap angle in radians and a correctly ordered tight-to-slack tension ratio.
What this chapter covers
- 01
Normal and tangential contact forces
- 02
Static friction inequality
- 03
Impending motion
- 04
Kinetic friction
- 05
Flexible-belt tension ratio
- 06
Comparing impending sliding with tipping
- 07
Separate friction demands and capacities at multiple contacts
- 08
A final contact-regime statement comparing demand with available capacity
Worked example · free
Angled pull at impending slip
- +1Predict rightward motion and draw friction left.
- +1Use vertical equilibrium to express the normal force in terms of the applied force.
- +1Apply limiting friction only because impending motion is stated.
- +1Use horizontal equilibrium and solve the coupled equation.
- +1Check that the horizontal pull component equals the limiting friction.
Key terms
- Static friction
- A self-adjusting tangential contact force bounded by a coefficient times the normal force.
- Impending slip
- The limiting state immediately before relative motion begins at a contact.
- Wrap angle
- The belt contact angle around a drum, measured in radians for the exponential tension relation.
- Friction demand
- The tangential force required by equilibrium at a contact.
- Friction capacity
- The maximum available static friction based on normal force and coefficient.
- Tight side
- The belt side carrying the larger tension at impending slip.
- Slack side
- The belt side carrying the smaller tension at impending slip.
- Tipping threshold
- The applied loading at which a contact resultant reaches the edge of the support region.
Friction and Flexible Belts FAQ
Is static friction always equal to coefficient times normal force?
No. Static friction takes the magnitude required for equilibrium up to its maximum value. Equality applies only at impending slip. First solve for the required friction and compare it with the available limit unless the wording explicitly states a limiting condition.
How do I choose friction direction?
Remove friction mentally and predict the relative motion that would occur at the contact. Friction on the chosen body opposes that threatened motion. For wheels or multi-body systems, a torque or cable may make this less intuitive, so state the prediction before drawing the arrow.
What are the key belt checks?
Convert the wrap angle to radians, place tight-side tension over slack-side tension and confirm the ratio exceeds one. The exponential belt relation describes impending slip on a rough contact, so name that regime rather than applying it to every belt problem.
How do sliding and tipping thresholds interact?
Calculate the applied load for impending sliding and separately calculate the load that moves the normal resultant to an edge for impending tipping. The smaller positive threshold identifies the first mode, provided the corresponding contact assumptions remain physically valid.
Assessment move
Practise identifying threatened motion before writing equations. Keep normal equilibrium separate from tangential equilibrium, and delay the limiting equality until the condition is justified. For belts, write the tight and slack sides on the diagram and check the tension ratio direction.
Create pairs of nearly identical crate problems, one asking whether rest is possible and one asking for the force that just initiates motion. The first requires a friction inequality and the second permits equality. Add upward and downward angled pulls so the normal-force change becomes visible.
For ladders, predict whether the base moves outward before drawing friction and compare sliding with tipping where both modes are possible. For wheels under couples, use the torque sense to determine threatened contact motion. In every multi-contact problem, assign a separate normal and friction limit to each interface. Convert belt angles to radians on a dedicated line and confirm the exponential ratio exceeds one.
Finish the answer with the regime: required static friction, limiting friction or kinetic friction, plus the corresponding motion direction. Add a friction-demand table to each solution: required tangential force, available static limit and conclusion. This separates a body that rests below the limit from one at impending slip.
Practise a two-block cable system where each contact has a different coefficient and verify that one interface may reach its limit first. For ladder questions, locate the normal reactions before assigning friction and check the no-friction tendency. For belt questions, reverse the proposed motion and show how tight and slack sides exchange roles.
Include one tipping comparison using moments about the edge, then select the smaller threshold between tipping and sliding. This builds a complete failure-mode answer instead of a single coefficient calculation.
