Inclined plane
A ramp problem. Gravity splits into a part along the slope and a part pressing into it.
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Analogy
A skier feels only the slope part pulling her downhill.
Example
a = g sin 30a = 9.8 x 0.5a = 4.9 m/s^2
In practice
On a frictionless 30 degree slope, a block accelerates at 4.9 m/s squared.
Practice
Flashcards
- On a frictionless slope at angle theta, what is the acceleration?a = g sin theta, down the slope.
Interview questions
- A 10 kg block slides down a 30 degree ramp with friction coefficient 0.2. Find its acceleration.
- Draw a free-body diagram
- Weight component along slope is mg sin theta
- Friction is coefficient times mg cos theta
- Net force over mass gives acceleration
Questions people ask
Why does the normal force on a slope equal mg cos theta?
The surface supports only the part of weight pressing into it. That part is mg cos theta, where theta is the slope angle. There is no acceleration into the slope, so the normal force balances that part. The other part, mg sin theta, pulls the block along the slope.
What angle makes a block start sliding?
A block begins to slide when the slope part of weight, mg sin theta, exceeds the maximum friction, coefficient times mg cos theta. This happens when tan theta equals the coefficient. A coefficient of 0.5 means it slides at about 27 degrees.