Motion on an Inclined Plane and Angle of Repose
On an incline of angle t, the body slides when tan t exceeds μs; the angle at which sliding just begins is the angle of repose.
What is Motion on an Inclined Plane and Angle of Repose?
On an incline of angle t, the body slides when tan t exceeds μs; the angle at which sliding just begins is the angle of repose.
Key formula / rule: N = mg cos t; driving component = mg sin t.
Key points
- Derive the angle of repose from the sliding condition.
- Compute acceleration for a block on a rough incline.
Common exam trap
Using N = mg on the incline.
Definitions
- Term
Motion on an Inclined Plane and Angle of Repose
- Meaning
On an incline of angle t, the body slides when tan t exceeds μs; the angle at which sliding just begins is the angle of repose.
- Term
Motion on an Inclined Plane and Angle of Repose — explanation
- Meaning
Resolving weight along and perpendicular to the incline gives mg sin t driving motion and N = mg cos t setting the friction limit. The mass cancels, so the condition to slide depends only on the angle and μs.
Learning objectives
Derive the angle of repose from the sliding condition.
Compute acceleration for a block on a rough incline.
Formulae
- Key point
N = mg cos t; driving component = mg sin t.
- Key point
Angle of repose: tan t = μs, independent of mass.
- Key point
Net acceleration down a rough incline: g(sin t - μk cos t).
Prerequisites
PHY-U1-NLM-T2-S1-C1
PHY-U1-KIN-T2-S1-C2
Common mistakes
Using N = mg on the incline.
Forgetting that friction reverses direction when the body is pushed up the slope.
Keywords
Motion
Inclined
Plane
Angle
Repose
Practice preview
If the angle of repose for a given pair of surfaces is 30 degrees, what is the coefficient of static friction between them?…
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A block is placed on an inclined plane. It just begins to slide down when the angle of inclination is theta. Which of the following conditions is true?…
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A block of mass M1 = 4 kg is placed on an inclined plane with an angle of inclination of 30 degrees. It is connected by a light string passing over a frictionless pulley to a second block of mass M2 = 3 kg, which hangs v…
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