Misconceptions in Mechanics

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2 Misconceptions in Mechanics Sharon Tripconey MEI Conference 2014

3 Sometimes, always or never true?

4 Sometimes, always or never true? Sort the cards into three piles For each of the three piles, order the cards so that the cards at the top are the statements that are least understood by learners. Keep the cards in their piles until the end of the session

5 Resultant force: what direction? A ball is projected vertically upwards. It rises through point D until it reaches its highest point E and then falls back down through F. Mark on the diagram an arrow which shows the direction of the resultant force acting at each position. Neglect air resistance E D F Extract from Mechanics in Action

6 What is gravity? It is the means by which objects with mass attract one another. Modern physics describes gravitation using the general theory of relativity, in which gravitation is a consequence of the curvature of spacetime which governs the motion of inertial objects. The simpler Newton's law of universal gravitation provides an accurate approximation for most calculations. F 1 F 2 m 1 m 2 r

7 F 1 F 2 m 1 m 2 r Let m 1 be the mass of the earth = kg Let r = radius of the earth = m G = Calculate the gravitational force of attraction that would act on a mass of 1 kg (at the earth s surface)

8 Some basic principles The mass of a body is the amount of matter in it. It is independent of location and is a scalar quantity. Gravitational attraction gives a body weight. The gravitational attraction of the Earth for a body is inversely proportional to the distance of the body from the centre of the Earth. At the Earth s surface, the weight of a body in N is mg where m is the mass of the body in kg and g is the acceleration due to gravity in m s -2. g=9.8ms -2 Weight depends to an extent on location and an object can have slightly different weights at different points on the earth s surface. The weight of a body acts through its centre of mass. This is a point that is at the centre of uniform bodies such as spheres, cubes, on the centre of the axis of symmetry of a circular cylinder etc Internal and external forces may act on a system weight is an external force mg

9 Force and motion You cannot actually see forces, but you can often see their effect. In most cases a body will be under the influence of several forces. Sketch the velocity time graph for the motion on the ball.

10 Motion Graphs Sketch the following graphs (for the ball s motion) velocity-time speed- time displacement time distance travelled - time distance time

11 velocity-time speed- time displacement time distance time distance travelled - time

12 Displacement, distance & distance travelled displacement 0 time

13 Displacement, distance & distance travelled distance displacement distance travelled 0 time

14 Making links - extending basic ideas The instantaneous acceleration is the gradient of the velocity time graph v m/s velocity time t s

15 Summary Motion Graph Gradient Area Notes Displacementtime Velocity Not significant Vertical axis can be positive or negative Velocity-time Acceleration Displacement Areas below the time axis represent negative displacement. v=0 indicates a possible change in direction Accelerationtime Rate of change of acceleration Velocity

16 Motion graphs activity

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18 Some Basic Principles Newton s first law (N1L) Every particle continues in a state of rest or uniform motion in a straight line unless acted on by a resultant external force. This means that for a particle to be in equilibrium* it must be the case that there is no resultant force acting on it (*dynamic or static equilibrium) Newton s second law (N2L) When a force acts on a particle, the change in momentum is proportional to the force. For constant mass, F = ma. Newton s third law (N3L) When one object exerts a force on another there is always a reaction that is equal in magnitude and opposite in direction to the applied force. This means that we expect forces to be found in pairs.

19 Force Diagrams A person in a lift

20 Bathroom scales and a broom Extract from Mechanics in Action

21 W = Weight of the person Assumptions: Each body is a particle in equilibrium The scales and the brush have zero mass W

22 W Weight of the person F Force exerted on the brush F S N Contact force (brush and floor) Contact force (person and scales) R Contact force (scales and floor) F N R W N W S Pairs of forces (N3L) R S

23 250kg (lift and person) 50kg (person) 200kg (lift)

24 250kg 50kg 200kg T T R 250g 50g R 200g

25 Total surface force on a car Each of the diagrams shows the total surface contact forces acting on the front and on the rear wheels of a car on a straight horizontal road. Air resistance should be neglected. For each case, suggest a scenario and the motion that could be taking place.

26 Coefficient of Friction According to Coulomb s model, is a constant for any pair of surfaces. Typical values for the coefficient of friction are given below: wood sliding on wood metal sliding on metal normal tyres on dry road 0.8 racing tyres on dry road 1.0 sandpaper on sandpaper 2.0 skis on snow 0.02

27 Rest a metre ruler on your fingers and gradually begin to draw your fingers together, what happens next? Can you explain?

28 Forces on the ruler R 1 R 2 F R F F W

29 Sometimes, always or never true?

30 Sometimes, always or never true? Firstly, sort the cards into three piles Then, for each of the three piles, order the cards so that the cards at the top are the statements that are least understood by learners. Keep the cards in their piles until the end of the session

31 Sometimes, always or never true? What would you do to try and address each of these statements? Are there any more statements that you would add to this set of cards? If so, what are they?

32 Forces come in pairs Always If the resultant force on a particle is zero then the particle is in equilibrium The weight of an object always acts vertically downwards

33 Never A graph of distance travelled against time can have a negative gradient At its maximum height a projectile has no overall force acting on it.

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