Inclined plane calculator
A ramp trades distance for force. The mechanical advantage is the ratio of ramp length to height.
Force needed to push it up
519.711 92N
- Gravity component along the ramp
- 335.407 18
- Normal force
- 921.523 66
- Friction force
- 184.304 73
- Acceleration if released
- 1.511 02 m/s2
- Ideal mechanical advantage
- 2.9238
Show the working
- Mass = 100
- Ramp angle = 20
- Coefficient of friction = 0.2
- theta = rad(20) = 0.349 066
- weight = 100 * g0 = 980.665
- Gravity component along the ramp = 980.665 * sin(0.349 066) = 335.407
- Normal force = 980.665 * cos(0.349 066) = 921.524
- Friction force = 0.2 * 921.524 = 184.305
- Force needed to push it up = 335.407 + 184.305 = 519.712
- Acceleration if released = (335.407 - 184.305) / 100 = 1.511 02
- Ideal mechanical advantage = sin(0.349 066) > 0 ? 1/sin(0.349 066) : 0 = 2.9238
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- along the ramp: m g sin(theta); normal: m g cos(theta)
- force to push up = m g sin(theta) + mu m g cos(theta)
- ideal mechanical advantage = 1 / sin(theta)