Mechanics in 2 dimensions

Mechanics The branch of physics concerned with motion. ‘kinematics’: describing motion ‘dynamics’: explaining motion in terms of forces acting on particles. Mechanics may take into account frames of reference.

Learning outcomes analyse projectile motion in terms of a vertical acceleration plus constant horizontal speed and use this to solve quantitative problems identify velocity & acceleration vectors at points on a projectile path describe the conditions for static equilibrium when several forces act on a rigid object analyse simple 2-D interactions using the law of conservation of momentum draw and interpret free body force diagrams to represent forces acting on a particle or an extended rigid body use Pythagoras’ theorem and trigonometry to resolve 2-D vectors into components and calculate resultants use the main trigonometric functions of a calculator

Teaching challenges Students need careful guidance, discussion and practice to understand what vectors and their components are (not only displacements, but also velocity, acceleration, angular displacement, angular velocity, force, field etc) construct vector diagrams understand functions sine, cosine and tangent add and subtract vectors quantitatively using trigonometry

Warm-up In pairs: 1 Articulate clearly Newton’s three laws of motion. 2 For each law: Clarify when (how) it applies, with a few concrete examples. 3 Write down the kinematic equations, again clarifying when each of them applies. These BIG IDEAS underpin analysis of motion in 2D. Refer teachers to the AP “Toolkit for computing” handout.

Trigonometric functions

Pythagoras

Adding perpendicular velocities A toy car with two motions: BIG IDEA: Velocities add as vectors. see VPL simulations Resolving vectors and Vectors At tables, teachers first do PP experiment A toy car with two motions.

Adding vectors graphically Procedure 1. Place tail of 2nd vector at tip of 1st vector. 2. Vector sum is found as tail of 1st to tip of 2nd. (a parallelogram) Try the Geogebra simulation. Geogebra animations, created by Roni Malek at SLC London for SASP Physics. http://slclondon.org.uk/files/SASP/ 9

Adding vector components Try VPLab simulations Resolving vectors and Vectors

Projectile motion Object launched in a uniform gravitational field. BIG IDEA: Vertical & horizontal motions are independent. vertically: uniform acceleration due to gravity horizontally: constant speed Demo with flicking coins, or ball bearings in collision.

Parabolic path of a projectile Velocity changes by the same downward amount in each interval of time.

Parabolic path of a projectile Throw ball in front of screen, so that its trajectory matches the parabola. Together study Multiflash photos of projectiles from Jim Jardine (1970) Mass in Motion Longmans. If available: show Water jet through rings.

Resultant force The need for a ‘free body force diagram’. Two tractors pull a barge along a straight canal. BIG IDEA: Forces add as vectors. The water will exert a drag force on the barge. What happens if the three forces are in equilibrium? Do 3 TAP experiments.

A closer look at the barge On a rigid body, a force can be applied with equal effect at any point along its line of action.

Block on an inclined plane

Distributed weight and resultant A ring. The resultant acts at its centre of mass C, which is in empty space!

Surface reaction & resultant Surface reaction is a distributed force, but it may be replaced for convenience by its resultant, Rn.

Momentum in 2 dimensions Linear momentum is conserved. BIG IDEA: Add momentum as vectors. see VPLab simulation 2D Collisions Discuss PP experiment Momentum interchanges with other objects, then Puck-photos.

Endpoints In pairs: Revisit the BIG IDEAS covered.