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Kinematics on Inclined Plane: Free Fall and Geometry

Learn about the kinematic equations of constant acceleration, free fall, and inclined plane geometry. Understand how to find the components of acceleration and solve problems involving objects on inclined planes.

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Kinematics on Inclined Plane: Free Fall and Geometry

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  1. Outline Free Fall and Inclined Plane • Kinematic Equations of Constant Acceleration • Free fall • Inclined Plane Geometry • Graph of Sin • Kinematics on an Inclined Plane

  2. The equations of motion The “equations of motion” Caution: These are correct only if ais constant!

  3. Recall from last lecture… x vi axt vf ax axt vi vi specified by problem

  4. graphically The equation of motion in graphical form x t

  5. Freefall Objects in free fall How far away from the Earth do you have to go before you are weightless? What is g out where the astronauts are? Space station orbital altitude is 365 km. Radius of earth is 6400 km. g(orbit)=g(surface)*(Rearth/r)^2 =10*(6400/6765)^2 =9 m/s^2 ! Nowhere near zero! It is experimentally true that objects near the surface of the Earth fall at nearly constant acceleration of a = 9.80 m/s2 (downward) If gravity is the only force on an object, it is said to be in free fall • Far from Earth’s surface, g < 9.8 m/s2 • Air resistance will also cause real acceleration to be < 9.8 m/s2 Near the surface of the earth, and neglecting air friction, this is a key example of uniformly accelerated motion

  6. The Gravity Vector • is a vector that points toward the centre of the Earth • The acceleration of an object in freefall is • The largest acceleration that gravity can give an object is • Gravity can cause an object to slide down a ramp • If the surface of the ramp is perpendicular to , an object on the ramp won’t be accelerated by gravity • If the surface of the ramp is parallel to , an object on the ramp is accelerated at

  7. Components • If the ramp is somewhere in between being perpendicular and parallel to , an object on the ramp is accelerated at some fraction of • The acceleration that an object on a tilted ramp experiences is the “component of that is parallel to the surface of the ramp”

  8. How to find Components Right angle Symbols for parallel and perpendicular Accelerations:

  9. Example QQ28: Sin(x) A block is sliding down an icy slope (no friction). The slope makes an angle of 30 to the horizontal. What is the magnitude of the acceleration experienced by the block?

  10. Example: Kinematics on an Inclined Plane Ex. Kinematics on an Inclined Plane On a level road, the magnitude of a particular car’s maximum acceleration is 6 m/s2. That car drives up a hill that makes an angle of 30 to the horizontal. If it starts at the bottom of the hill at 10 m/s, how far will it travel in 10 seconds if it is accelerating as much as it can? • 0.16 km • 0.6 km • 1.6 km • 2.5 km

  11. Do for next class: • Read: Sections 3.3, 3.4 • Suggested problems: 3.9, 3.13

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