Given data
Step 1: Name the forces.
Weight points straight down: m g. The normal force acts perpendicular to the surface, and kinetic friction f opposes the motion up the slope.
math-science-homework
byRiley Musgrave
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Col 1–3: the problem
A 2.5 kg block slides down a 30° incline, μ = 0.15. Find its acceleration.
- Mass, m
- 2.5kg
- Incline angle, θ
- 30°
- Coefficient of friction, μ
- 0.15
- Unknown
- a
Col 4–12: the method
Show methe steps.
math-science-homework · any studentMath · Science
col 4–12: the method
The method, step by step
Every solution is numbered.
A preview of how an explanation arrives: each step labelled, sequenced and checkable, so you can follow the method instead of copying an answer. Scroll the column to move the marker.
Algebra
Step 2: Resolve along the slope.
Only the components along the incline drive the motion: m g sin 30° down the slope, minus f up the slope. The perpendicular components balance.
Algebra
Step 3: Use the friction model.
On the incline the normal force equals m g cos 30°, so f = μ m g cos 30°. The mass cancels out of the equation.
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Step 4: Solve for the unknown.
a = g (sin 30° − μ cos 30°). Substitute g = 9.8 m/s² to get a in metres per second squared. Check the signs and units before trusting the number.
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