Inclined plane & friction
A block on a slope you can tilt, with static and kinetic friction, and an optional applied force.
Rigid body mechanics — Forces, momentum and energy acting on bodies, and what happens when they collide.
Experiments already set up on it
Find μₛ by tilting
Raise the slope until the block slips. tan of that angle is μₛ.
- Static friction adjusts itself up to a maximum of μₛ N
- The slipping angle gives μₛ directly: its tangent is μₛ
Sliding with friction
A block released on a 30° slope. a = g(sin θ − μₖ cos θ).
- Resolving weight along and perpendicular to a slope
- Kinetic friction is independent of speed and of contact area
Frictionless ramp
No friction: a = g sin θ, and the speed at the foot follows v² = 2gh.
- a = g sin θ
- Energy conservation on a ramp: ½mv² = mgh
Energy lost to friction
Compare the kinetic energy at the foot with mgh lost on the way down.
- Work done against friction equals μₖ N d
- Mechanical energy is not conserved when friction acts
Pulling the block up
A steady force up a rough slope. How big must it be to move the block at all?
- The force needed to start motion exceeds the force needed to keep it going
- Adding forces along a slope
What you can measure
Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.
- Timet (s)
- Distance down the slopes (m)
- Distance travelledd (m)
- Velocity along the slopev (m/s)
- Speed|v| (m/s)
- Accelerationa (m/s^2)
- Height above the footh (m)
- Horizontal positionx (m)
- Vertical positiony (m)
- Normal contact forceN (N)
- Friction forceF_f (N)
- Net force down the slope before frictionF_∥ (N)
- Is it moving?M
- Kinetic energyEₖ (J)
- Potential energyEₚ (J)
- Mechanical energyE (J)
What you can change
Any of these can be the thing you vary, and every combination of the ones you choose is run as its own trial.
- Slope angleθ (°)
- Slope lengthL (m)
- Starting distance down the slopes₀ (m)
- Massm (kg)
- Initial speed down the slopev₀ (m/s)
- Applied force up the slopeF (N)
- Coefficient of static frictionμ_s
- Coefficient of kinetic frictionμ_k
- Gravitational field strengthg (m/s^2)
The equations behind it
What inclined plane & friction is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.
Forces and momentum
- Newton’s second law
- Momentum
- Force as a rate of change of momentum
- Impulse
- Static friction — At most this, until it slips.
- Dynamic friction
Work, energy and power
- Work done by a force
- Kinetic energy
- Change in gravitational potential energy — Near the surface, where g is constant.
- Elastic potential energy
- Power
- Efficiency
Also in Rigid body mechanics
Collisions
Two pucks on a frictionless surface: head-on or glancing, elastic through to perfectly inelastic.
Rotational dynamics
A flywheel driven by a motor or a falling mass, with the turns counted for you: τ = Iα, measured rather than assumed.
Moments & equilibrium
A loaded plank on two supports, with the force on each one measured: take moments, and find where it balances or tips.
Circular motion
A conical pendulum whirling on a string: the tension holds the bob up and pulls it round, and only one speed keeps the angle steady.