Practice

Newton’s second law, friction and ramps

Net force and acceleration on level floors, ramps and a cart pulled by a hanging block, with kinetic and static friction.

The skill

Start with a free-body diagram, choose the system and a positive direction, add the force components along that direction to get $F_{net}$ , and divide by $m_{sys}$ . On a ramp, tilt your axes so one runs along the incline; the weight then splits into $m g \sin θ$ along the ramp and $m g \cos θ$ into it. Kinetic friction is $μ_{k} F_{n}$ , while static friction takes whatever value keeps the surfaces from sliding, up to $μ_{s} F_{n}$ . Students most often write $F_{n} = m g$ on a ramp, where the normal force balances only the perpendicular part of the weight.

A worked example

A 0.60 kg block slides down a frictionless ramp inclined at 30° above the horizontal. Use g = 10 m/s².

What is the magnitude of the block's acceleration, in m/s²? Give your answer to three significant figures.

Solution

Only two forces act: the weight mg straight down and the normal force perpendicular to the ramp. The normal force has no component along the ramp.
The component of the weight along the ramp is mg sin 30°, so $a_{s y s} = F_{n e t} / m_{s y s}$ = (mg sin 30°) ÷ m = 10 sin 30° = 5.00 m/s².
The mass cancels, so a heavier block on the same ramp has the same acceleration.

Answer: 5

Newton’s second law, friction and ramps

The skill

A worked example

Solution

Your turn

Lessons behind these problems