DPST1021 Chap.4 Friction, Inclined Planes and Drag
Friction, Inclined Planes and Drag
Week 3 of Physics 1A opens with Lecture 7 on friction and inclined surfaces, then starts Lecture 8 with the drag force. Together they extend Newton's laws from idealised smooth surfaces to the contact forces that real objects feel.
Friction is modelled with two coefficients: a static one that caps how hard a surface can grip before anything slips, and a kinetic one that fixes the resisting force once sliding is under way.
The lecture outcomes ask for three things. First, calculating a coefficient of kinetic friction from the forces on a moving body, or the reverse.
Second, finding the static friction force in situations where it is below its limit, and the static coefficient when it is exactly at its limit. Third, analysing objects on inclined surfaces that are stationary, accelerating or moving at constant velocity.
Tilted axes, with one along the slope and one across it, make all three cases manageable, and the same geometry underpins Lab 2, Static Friction on an Inclined Plane.
Drag, the third resistive idea, closes the chapter. Unlike sliding friction, air resistance grows with speed, so a falling body eventually reaches a terminal speed at which drag balances its weight and the acceleration vanishes.
These ideas belong to the mechanics block assessed in Test 1, and they return in the following chapter, where the work done by friction becomes the energy lost from a moving system.
What this chapter covers
- 01
Static friction: a force that takes any value up to the product of the static coefficient and the normal force, found from the force balance whenever nothing slips.
- 02
Kinetic friction: a constant resisting force equal to the kinetic coefficient times the normal force, acting opposite to the sliding velocity once motion has begun.
- 03
Normal force on a ramp: the perpendicular contact force, equal to mg cos theta only when no other force pushes into or lifts away from the slope.
- 04
Slip angle on a ramp: the steepest tilt at which a block can stay at rest, where the tangent of the angle equals the static coefficient.
- 05
Sliding on an incline: the downhill acceleration g(sin theta minus the kinetic coefficient times cos theta), which reduces to zero for constant-velocity sliding.
- 06
Drag and terminal speed: a speed-dependent air resistance that grows until it matches the weight, giving a steady maximum speed for a falling body.
Worked example · free
Pushing a box up a ramp at steady speed
- 1Compare the slope with the critical angle: tan 20° = 0.36, below the static coefficient 0.50, so the box can stay at rest without slipping.
- 1At rest the friction balances the downhill weight component exactly: f = mg sin 20° = 4.0 × 9.80 × 0.342 = 13.4 N, pointing up the slope. It is not 0.50N.
- 1Moving uphill, kinetic friction points down the slope with size 0.35 × mg cos 20° = 0.35 × 36.8 = 12.9 N.
- 1Constant speed means zero net force along the slope: F = mg sin 20° + fk = 13.4 + 12.9 = 26 N.
Key terms
- Coefficient of static friction
- A dimensionless number that sets the largest friction force a surface pair can supply before slipping, as a fraction of the normal force.
- Kinetic friction
- The resisting contact force between surfaces that are sliding relative to each other, roughly independent of speed and contact area.
- Critical angle
- The incline angle at which a resting block is just about to slip, where the tangent of the angle equals the static coefficient.
- Terminal speed
- The constant speed a falling body settles at once air resistance has grown to equal its weight, so the net force is zero.
Friction, Inclined Planes and Drag FAQ
Does a heavier block slide down a ramp more easily?
Not in the simple friction model. Both the downhill weight component and the maximum friction are proportional to mass, so mass cancels from the condition for slipping and from the sliding acceleration. A heavy and a light block made of the same material start to slip at the same tilt and speed up at the same rate once moving.
Why is the kinetic coefficient smaller than the static one?
Surfaces at rest have time to settle into each other, so microscopic contact points bond more strongly. Once sliding, those contacts keep breaking before they fully form. That is why a heavy wardrobe needs a large shove to start moving, then becomes noticeably easier to keep going across the floor.
Which way does friction point on an incline?
It opposes the relative motion, or the motion that would occur without friction. A block resting on a ramp tends to slide down, so static friction acts up the slope. If you push the block uphill, kinetic friction points down the slope, adding to the weight component you must overcome.
Does a skydiver at terminal speed have zero velocity?
No. Terminal speed means zero acceleration, not zero motion. Drag equals weight, so the net force is zero and the velocity is constant. Opening a parachute increases the area and drag coefficient, which lowers the terminal speed to a safe landing value.
Exam move
Draw a free-body diagram for every friction problem before touching a formula, and label each force with what exerts it. Next, decide whether the surfaces are slipping; that single decision tells you whether friction comes from the force balance or from a coefficient times N. For inclines, tilt the axes so that one lies along the slope, then write Newton's second law separately along and across the surface.
Practise the three standard cases side by side: block at rest, block sliding at constant velocity, block accelerating, and notice how each changes one line of algebra. For drag, set weight equal to drag and solve for the terminal speed, checking how it scales with mass and area. Finally, repeat the Lab 2 reasoning on paper: predict the slip angle for a given static coefficient and explain why the block's mass does not matter.
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