Download BIG IDEA

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.
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.
Trigonometric functions
opposite
hypotenuse
adjacent
cosq =
hypotenuse
opposite
tanq =
adjacent
æ opposite ö
-1
q = sin ç
÷
è hypotenuse ø
sinq =
Pythagoras
a b c
2
2
2
Adding perpendicular velocities
A toy car with two motions:
BIG IDEA: Velocities add as vectors.
see VPL simulations Resolving vectors and Vectors
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.
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
Parabolic path of a projectile
Velocity changes by the same downward amount
in each interval of time.
Parabolic path of a projectile
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?
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
Endpoints
In pairs:
Revisit the BIG IDEAS covered.