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When the acceleration is constant, motion is described in terms of relationships between measurable scalar and vector quantities, including displacement, speed, velocity, and acceleration. Motion under constant acceleration can be described quantitatively using the following formulae: v = v0 + at s = v0t + ½at2 v2 = v02 + 2as Projectile motion can be analysed quantitatively by treating the horizontal and vertical components of the motion independently.
vH = v cos θ and vV = v sin θ
for the horizontal and vertical components respectively.
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Explanation of the difference between scalar and vector quantities and methods of measurement of these quantities is covered in Stage 1, Topic 1: Linear motion and forces. This uses the concept of acceleration developed in Stage 1, Subtopic 1.1: Motion under constant acceleration. Use trigonometric calculations and scale diagrams to determine quantities, using vector addition and subtraction. Given a diagram showing the path of a projectile to show the forces acting on the projectile, as well as the acceleration and velocity vectors. Use a projectile launcher to investigate the effect of launch angle or launch height on range. |
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Momentum is a property of moving objects and is defined as the product of the mass and the velocity of the object. It is conserved in an isolated system and may be transferred from one object to other objects when a force acts over a time interval. Kinetic energy is a property of moving objects and is given by the formula Ek = ½mv2 Newton's Second Law of Motion can be expressed as two formulae: F = ma F = ΔpΔt
where p = mv is the momentum of the object. Derive ΔpΔt by substituting the defining formula for acceleration
a = ΔvΔt
into Newton's Second Law of Motion, F = ma, for particles of fixed mass. (The net force, F, and hence the acceleration, a, are assumed to be constant. Otherwise, average or instantaneous quantities apply.) Draw vector diagrams in one dimension or in two dimensions (with right-angled or equilateral triangles) in which the initial momentum is subtracted from the final momentum, giving the change in momentum, Δp Solve problems (in both one dimension and two dimensions) using the formulae: F = ma, p = mv, F = ΔpΔt
and Ek = ½mv2 |
Many of these ideas have been introduced in Stage 1 through one-dimensional situations. The focus here should be on two-dimensional situations. Consider the development of the discovery of neutrinos. This uses the concepts of acceleration and force developed in Stage 1, Subtopics 1.1: Motion under constant acceleration and 1.2: Forces. Use the conservation of momentum to determine the change in velocity during firing it into a trolley. Investigate how the law of conservation of momentum was used to predict the existence of neutrinos. Explore perspectives in the public debate about the economics of space exploration. Is government funding likely to be maintained? Research the most appropriate types of spacecraft propulsion for journeys to different destinations, considering technical challenges and speculative technologies. |
