Problems Plus 7: The Physics of a Block on an Inclined Plane

In this video I go over the physics of a solid block on an inclined plane in terms of the sliding friction, weight, normal force, and applied horizontal force. At an incline angle just before the block starts to move down, the friction force is proportional to the normal force and related to it by the coefficient of static friction. I first determine this coefficient by summing up the forces and equating to zero, and the coefficient becomes equal to the tangent of the max angle before sliding. I then determine the minimum horizontal force that can be applied as we increase the incline angle even further, while the block still doesn't move. Lastly, I calculate the maximum horizontal force before the block moves. In this case, the friction force is in the reverse direction. At an angle between 90 degrees and (90 - sliding angle), the horizontal force can approach infinity and the block still won't move up the inclined plane, because the normal force (and hence friction) also approaches infinity completely countering the horizontal force.

Timestamps:

- Problem 7: Block on an inclined plane: 0:00
- Solution to (a): Coefficient of static friction: 4:42
- Sum of forces on the block is zero: 5:27
- Obtaining coefficient of friction using trigonometry: 8:13
- Solution to (b): Find minimal horizontal force to not move the block: 9:31
- Rotate the system of forces to make the inclined plane flat: 11:50
- Writing the forces as components parallel and perpendicular to the inclined plane: 14:52
- Summing components and equating to zero: 19:16
- Solution to (c): Obtain formula for the minimum horizontal force: 23:30
- Apply the tangent double angle identity: 29:07
- Equation sounds reasonable: 30:07
- Solution to (d): Find maximal horizontal force to not move the block: 33:58
- Plot forces (friction force is negative) and rotate system to make inclined plane flat: 36:11
- Sum forces and equate to zero: 38:01
- Apply the tangent double angle trig identity: 44:10
- Formula sounds reasonable: 45:04
- Max horizontal force is just the min force but to the left by 2 sliding angles: 46:24
- Max force goes to infinity and block doesn't move when angle is 90 minus sliding angle: 49:19
- Normal force increases to infinity as well as horizontal force increases to infinity: 52:31

Video notes and playlists:

- HIVE notes: https://peakd.com/hive-128780/@mes/jlgigkdl
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_7Jd6ZORHFQMk8jbwmkos
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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