Motion, Forces and Energy - PDF

1 Motion, forces and energy 1.1 Physical quantities and measurement techniques How to determine an average value for a small distance ? Micrometer: Length of the object = 2.5 mm + (33/100) mm = 2.83 mm The precision of micr...

1 Motion, forces and energy 1.1 Physical quantities and measurement techniques How to determine an average value for a small distance ? Micrometer: Length of the object = 2.5 mm + (33/100) mm = 2.83 mm The precision of micrometer is 0.01 mm Question: Determine an average value for a short interval of time by measuring multiples Question: Scalar quantity: A scalar quantity has magnitude (size) only. Examples: Distance, speed, time, mass, energy and temperature.  Vector quantity A vector quantity has magnitude and direction. Examples: Displacement, force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength Determine, by calculation or graphically, the resultant of two vectors at right angles: Graphical method: Question: Question: 1.2 Motion Distance: Unit: cm, m  Displacement: Unit: cm, m Question: Solution: Example: Speed: It is the distance travelled per unit time. Velocity: Velocity is the change in displacement per unit time. Unit: m/s Question: Now let's consider the motion of a physics teacher. The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity. Solution: The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s. Acceleration: Question: Solution: Question: Solution: Example-1: t(s) 0 1 2 3 v(m/s) 5 5 5 5 No change in velocity, no acceleration Uniform velocity, displacement changes uniformly. Example-2: t(s) 0 1 2 3 v(m/s) 0 5 10 15 Velocity changes uniformly, so uniform acceleration or constant acceleration. Uniform acceleration means change in velocity per unit time is constant. Example-3: t(s) 0 1 2 3 v(m/s) 0 5 12 21 Velocity changes non-uniformly, so non-uniform acceleration. Non-uniform acceleration means change in velocity per unit time is not constant. Example of increasing acceleration. Example-4: t(s) 0 1 2 3 v(m/s) 0 5 9 12 Velocity changes non-uniformly, so non-uniform acceleration. Non-uniform acceleration means change in velocity per unit time is not constant. Example of decreasing acceleration. This is not deceleration. Example-5: t(s) 0 1 2 3 v(m/s) 15 10 5 0 Velocity decreases. Example of deceleration. Deceleration is a negative acceleration. Velocity changes uniformly, so uniform acceleration. Distance–time graphs: Gradient of the graph = speed Gradient = 0, so speed = 0 The object is stationary Acceleration = 0  Gradient constant, so speed constant The object is moving with constant speed Acceleration = 0  Increasing gradient, so increasing speed The object is accelerating  Decreasing gradient, so decreasing speed The object is decelerating Question: Question: Speed–time graphs: Gradient of the graph = acceleration Area under the graph = distance travelled The object is at rest Gradient = 0, so acceleration = 0 Area under the graph = 0, so distance travelled = 0  The object is moving with constant velocity Gradient = 0, so acceleration = 0 Distance travelled = area of the rectangle  Velocity increase uniformly Gradient = constant, so acceleration = constant Distance travelled = area of the triangle  Velocity increases uniformly Gradient = constant, so acceleration = constant Distance travelled = area of the trapezium  Velocity increases non-uniformly Increasing gradient, so increasing acceleration  Velocity increases non-uniformly Decreasing gradient, so decreasing acceleration This is NOT deceleration The acceleration of free fall g for an object near to the surface of the Earth is approximately constant and is approximately 9.8 m / s2 Question: Question: Question: Question: Question: Question: Question: Question: 1.3 Mass and weight Mass: Mass is a measure of the quantity of matter in an object at rest relative to the observer. The mass of an object resists change from its state of rest or motion (inertia) More mass, more inertia Units: g, kg Gravitational field: A gravitational field is a region in which a mass experiences a force due to gravitational attraction. Weight: The weight of an object is the gravitational force experienced by the object. Unit: N  Gravitational field strength: Gravitational field strength is a force per unit mass. This is equivalent to the acceleration of free fall (g =9.8 m/s2) Differences between mass and weight: Know that weights, and therefore masses, may be compared using a beam balance or equal-arm balance Mass is measured using an electronic balance: Weight is measured using a force meter: Question: 1.4 Density Density: Density as mass per unit volume. Unit: kg/m3 Question: The density of water is 1000 kg/m3. What do you mean by this? Answer: The mass of 1m3 of water is 1000 kg. Do not need to memorise these. Just have a look.  An experiment to determine the density of a liquid Measure the mass of an empty beaker using an electronic balance. Measure the mass of the liquid and the beaker using the electronic balance. From the difference of the above two measurements we can find the mass of the liquid. Measure the volume of the liquid using a measuring cylinder. Dividing the mass of the liquid by the volume of the liquid, we can find the density of the liquid, because. An experiment to determine the density of a solid which sinks in a liquid (volume by displacement) Measure the mass of the solid using an electronic balance. Measure the volume of the liquid using a measuring cylinder. Measure the volume of the liquid and the solid using the measuring cylinder. From the difference of the two volumes, we can find the volume of solid. Dividing the mass of the solid by the volume of the solid, we can find the density of the solid, because. Question: 1.5 Forces 1.5.1 Balanced and unbalanced forces  Different types of forces: Contact forces: Contact forces occur between objects that are touching each other. Examples: 1. Friction, drag, air resistance 2. Tension (elastic force) 3. Thrust (driving force)  Friction: Friction is a force that impedes motion. Friction between two moving surfaces produces heating. Friction is a resistive force because it acts in the opposite direction to motion. Friction does not only oppose motion between solid surfaces. Objects moving through a liquid or a gas experience friction too. In liquids and gases, friction is usually called drag.  Drag: Drag depends on speed, when speed increases drag also increases. There is no drag on a stationary object. Drag always acts in the opposite direction of motion. Tension (elastic force): Tension is an elastic force that occurs in a string or spring. Thrust (driving force): It is a driving force which moves an aircraft or any vehicle.  Non-contact forces: Non-contact force is a force applied to an object by another body that is not in direct contact with it. Non-contact forces come into play when objects do not have physical contact between them. Examples: 1. Weight (gravitational force): The weight of an object is the gravitational force experienced by the object. 2. Electrostatic force: The electrostatic force is the force of attraction or repulsion between two charged particles. 3. Magnetic force: The magnetic force is a force between two magnetic poles or between moving charges. Question:  Free-body diagram Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. It is required to know the resultant force on the object.  Newton’s first law: An object either remains at rest or continues to move in a straight line at constant speed unless acted on by a resultant force. To change either magnitude (speed) or direction of velocity, resultant force is required. Question: Inertia: Every object is reluctant to change its state of rest or state of motion. Inertia is the term used to describe this phenomenon. The mass of an object is responsible for inertia. Inertia is the resistance of an object to changes in its motion. It is directly proportional to the mass of the object. Therefore, objects with greater mass have a greater tendency to resist changes in their velocity or direction. Question: Solution: Resultant force = 0 Acceleration = 0 Forces are balanced. If the object is stationary, it will remain stationary. If the object is in motion, it will continue to move with constant velocity. Magnitude and direction of velocity will not be changed. Question: Question: Solution: Resultant force is not zero Acceleration is not zero Forces are not balanced Resultant force = 24N - 10N = 14N Velocity will change. How to find acceleration? To find acceleration we use the following equation. Question:  Solution: Resultant force = (24 + 10) N = 34 N = constant Acceleration = constant Velocity changes uniformly Question: Solution: Question: Question: Newton’s third law: When object A exerts a force on object B, then object B exerts an equal and opposite force on object A. Remember: Earth has greater mass than the Moon, still they apply equal forces on each other. Pair of number 1 force (gravitational force on the book by the earth): Gravitational force on the earth by the book. Pair of number 2 force (contact force on the book by the table): Number 3 force, contact force on the table by the book. Pair of number 4 force (contact force on the table by the floor): Contact force on the floor by the table. Pair of number 5 force (gravitational force on the table by the earth): Gravitational force on the earth by the table. Question: Question: 1.5.2 Friction  Friction: Friction is a force that impedes motion. Friction between two moving surfaces produces heating. Friction is a resistive force because it acts in the opposite direction to motion. Friction does not only oppose motion between solid surfaces.Objects moving through a liquid or a gas experience friction too. In liquids and gases, friction is usually called drag.  Drag: Drag depends on speed, when speed increases drag also increases. There is no drag on a stationary object. Drag always acts in the opposite direction of motion. The motion of objects acted on by a constant weight or driving force, without drag: Only force acting on the object is gravitational force. So acceleration will be 9.8 m/s2 Every second velocity increases by 9.8m/s The motion of objects acted on by a constant weight or driving force, with drag (including air resistance or resistance in a liquid): Remember: Drag increases then becomes constant because speed increases then becomes constant. Acceleration decreases to zero because resultant force decreases to zero. A car can also reach terminal velocity when drag force becomes equal to the driving force. (when resultant force = 0) Question: Question: The thinking distance, braking distance and stopping distance of a moving vehicle:  Thinking distance depends on: Human reaction time: Mental state, tiredness, alcohol, drugs. When human reaction time increases, thinking distance also increases. Speed of the vehicle: More speed means more thinking distance.  Braking distance depends on: Braking force: More braking force means less braking distance. Tyre surface and road conditions (friction): When friction between tyre and road decreases, the braking distance increases. Mass of the vehicle (Load): More load means more inertia of motion, so more braking distance. Speed of the vehicle: More speed of the vehicle means more braking distance. Question: Question: Question: 1.5.3 Elastic deformation Remember: Forces may produce a change in size and shape of an object. Hooke’s law: An experiment to investigate the relationship between force (load) and the extension of a spring: Limit of proportionality: It is a point beyond which the extension is no longer directly proportional to the load. So up to the limit of proportionality, the object obeys Hooke’s law: Spring constant: It is the force required for unit extension. Unit: N/m or N/cm Question: The spring constant of a spring is 10N/cm. What do you mean by this? Answer: The spring will extend by 1 cm when 10 N load is applied. Question: The spring constant of a spring is 10 N/cm and the spring constant of another spring is 200 N/cm. What spring is stiff or tough? Answer: The second spring is tough because more force is required for same extension. Remember: Spring constant determines the stiffness of a spring. More spring constant means more stiff or tough. Question: 1.5.4 Circular motion Remember: When an object is moving in a circular path with a constant speed. Velocity is a vector quantity. Here magnitude of velocity is constant but direction changes every moment. So velocity is not constant. Acceleration is not zero. Resultant force can not be zero. A resultant force is required to change the direction of velocity. This resultant force always acts towards the centre of the circular path. The force is always perpendicular to the direction of velocity. The direction of force changes as a result the direction of acceleration also changes. The direction of acceleration is always in the direction of the resultant force, i.e. towards the centre of the circular path. When speed increases, inertia also increases. So more force is required while turning in a circular path, provided that mass of the object and radius of the circular path are remain same. When radius decrease, more change in direction of velocity. So more force is required while turning in a circular path, provided that mass of the object and the speed of the object are remain same. When mass increases, inertia also increases. So more force is required while turning in a circular path, provided that speed of the object and radius of the circular path are remain same. Question: Question: Question: Question: 1.5.5 Turning effect of forces  Moment of a force: The moment of a force is a measure of its turning effect. A force acting on an object can cause the object to turn. This effect is known as the turning effect of a force. An example of this can be seen when we open a door. We apply a force to swing the door about its hinge. Definition: The moment of a force = force × perpendicular distance of the line of action of the force from the pivot. Unit: Nm d = perpendicular distance of the line of action of the force from the pivot. Question: Question: Solution:  Special case: The moment of the force F = F X 0 = 0 The line of action of the force passes through the pivot. Perpendicular distance of the line of action from the pivot is 0. The object will not rotate. The principle of moments : Question: The object is in equilibrium. Find the value of F. Solution: Question: Solution: Question: The object is in equilibrium. Find the value of F. Solution: Question: Question: Question: Question: An experiment to verify the principle of moments: Procedure: Balance a metre rule at its center, adding plasticine to one side or the other until it is horizontal. Hang unequal loads m1 and m2 from either side of the pivot and alter their distances d1 and d2 from the centre until the ruler is again balanced. Calculate the weights of the loads using the equation, W = mg. The weight of the load m1 is F1 and the weight of the load m2 is F2. Record the value of the distances d1 and d2. Calculate the anticlockwise moment F1X d1 and clockwise moment F2 X d2 Repeat the above steps using the same loads for different distances. The results should show that the anticlockwise moment equals the clockwise moment. 1.5.6 Centre of gravity Centre of gravity: It is the point through which all of an object’s weight can be considered to act. The centre of gravity of a uniform ruler is at its centre and when supported there it can be balanced, as shown in fig (a). If it is supported at other point it topples because the moment of its weight W about the point of support is not zero, as in fig (b). Question: An experiment to determine the position of the centre of gravity of a plane lamina using a plumb line: The effect of the position of the centre of gravity on the stability of simple objects: Question: 1.6 Momentum Momentum: Momentum = mass × velocity Question: Solution: Question: Solution: Impulse: Question: Solution: The principle of the conservation of momentum: Question: Solution: Question: Solution: Resultant force: Question: Solution: Question: Solution: 1.7 Energy, work and power 1.7.1 Energy Different stores of energy: Transfer of energy between stores: The principle of the conservation of energy: Example: An ideal pendulum swinging: Example: Hammering a nail: Question: The equation for kinetic energy, Question: The equation for the change in gravitational potential energy, Question: Question: Question: Question: 1.7.2 Work Work done: Question: Question: Question: Question: 1.7.3 Energy resources Question: Question: 1.7.4 Efficiency Question: Solution: Question: Solution: Question: Question: 1.7.5 Power Question: Question: Question: 1.8 Pressure Pressure: Question: Question: Solution: The pressure at a surface produces a force in a direction at right angles to the surface and an experiment to show this: The pressure beneath the surface of a liquid changes with depth of the liquid: The pressure beneath the surface of a liquid changes with density of the liquid: The equation for the change in pressure beneath the surface of a liquid: Question: The height of a liquid column in a liquid barometer may be used to determine the atmospheric pressure: Question: Question: Question: