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Frictionless Incline

Part of the Mechanics section of Coddy's Physics journey. Lesson 22 of 97.

On a frictionless ramp only gravity acts along the slope, so the mass cancels:

a=gsin⁡θa = g\sin\theta

A cart on a frictionless 30 degree ramp with only two forces, its weight mg straight down and the normal force N perpendicular to the ramp; its acceleration a points down along the slope

No friction: only mg and N act, and the acceleration points down the slope.

On a 30∘30^\circ ramp a=4.9 m/s2a = 4.9\ \mathrm{m/s^2}, for every mass. A rope pulling up the slope with FF adds a term: F−mgsin⁡θ=maF - mg\sin\theta = ma.

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Challenge

A winch pulls a 50 kg50\ \mathrm{kg} cart up a frictionless 30∘30^\circ ramp with a rope parallel to the slope. The rope pulls with TT = 300 N300\ \mathrm{N}. Find the acceleration aa of the cart.

Try it yourself

Physics diagram: ramp, cart, vec; arrows v

Solve for aa

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