Physics·Laws of Motion

Inclined Plane Simulator — Block on a Wedge with Friction

Adjust the incline angle, mass, and friction. See the full free-body diagram and watch the block slide.

mg (weight)

N (normal)

f (friction)

mg sinθ

Right-click drag = draw arrow · single-click = mark

θ30°

m2.00 kg

mg19.62 N

N = mg cosθ16.99 N

mg sinθ9.81 N

μ_s / μ_k0.20 / 0.15

Friction f2.55 N

Accel a3.63 m/s²

Sliding — tanθ > μ_s

Incline angle30°Mass2kgStatic μ_s0.2Kinetic μ_k0.15

A block on an inclined plane is the workhorse of Newtonian mechanics — every friction and equilibrium problem eventually reduces to one. Decompose gravity along and perpendicular to the surface, add the normal reaction, add friction if the block wants to move, and Newton's second law along the incline gives the acceleration. Slide the angle, mass, and coefficient of friction. Toggle the FBD to see the four forces (mg, N, mg sinθ, f) drawn on the block.

Key equations

Along the incline

$ma = mg\sin\theta - \mu_k mg\cos\theta$

Perpendicular to the incline

$N = mg\cos\theta$

Condition for sliding

$\tan\theta > \mu_s$

Acceleration down the incline

$a = g(\sin\theta - \mu_k \cos\theta)$

Key ideas to remember

1
Decompose gravity into two components: $mg\sin\theta$ along the incline (drives motion) and $mg\cos\theta$ into the incline (balanced by $N$ ).
2
The block stays at rest as long as $\tan\theta \le \mu_s$ — geometry alone, no numbers needed.
3
On a frictionless incline, acceleration is $g\sin\theta$ regardless of mass — same result Galileo used on his ramps.
4
Kinetic friction acts opposite to motion, so it flips sign if the block is pushed up the incline instead of released from rest.

Inclined Plane Simulator — Block on a Wedge with Friction

Key equations

Key ideas to remember

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