IGCSE Double Award Extended Coordinated Science

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1 IGCSE Double Award Extended Coordinated Science Physics 2.1 & 2.2 & 2.3 & Matters and Forces Mass and Weight You need to know what mass and weight are. Mass is the measure of amount of matter in an object. - Unit for mass is kilograms (kg) or grams (g). - All objects have mass - Even the smallest particles like electrons have mass. - Mass never changes (unless a part of the object is removed) and remains constant throughout the universe. - Mass is also the property that resists change in motion - This is known as inertia (more in Unit P2.3) - Change in motion is change in direction and/or speed ( velocity ), which means it is an acceleration. - So we can say mass is the property that resists acceleration - So more mass means smaller acceleration Weight is the force on the mass due to gravity. - Weight is a force, so it is measured in units of newtons (N) (more in Unit P2.3) - Weight is calculated by the formula w = mg - Where g stands for acceleration due to gravity or the gravitational field strength - The acceleration due to gravity (in freefall) is different depending on the environment. - Earth has acceleration due to gravity of about 10m/s 2, on the moon it is about 1.6m/s 2. - This means an object of mass 10kg, will have weight 100N on Earth, and 16N on the moon. - Weight is dependant on the gravitational field strength.

2 Density You need to know what density is, and how to find experimentally calculate density. Density how closely packed the matters are in an object (how dense an object is), or, - the measure of matter per volume - Density = mass volume - d = m v - kg/m 3 = kg m 3 for larger objects - g/cm 3 = g cm 3 for smaller objects For liquids or regularly shaped solids, it is fairly simple to calculate density. - Measure the mass using a scale, - Measure and calculate the total volume (for solids using the appropriate formula) - Then simply use the formula: density = mass / volume For irregularly shaped solids, the volume is harder to measure. - For example, a random pebble from the ground. - We use water displacement to find the volume - There are two methods. 1. Measuring cylinder method: - Fill a measuring cylinder with water and measure the initial volume - Then drop the irregular object in the cylinder - Measure the final volume. - The difference in volume is called the displaced volume and is equal to the volume of the solid. 2. Eureka can method: Eureka can is a special apparatus used to measure volumes of irregular solids. It is a large can with a single hole with a pipe to collect the displaced liquid - Completely fill the Eureka can up to the hole - Place a measuring cylinder below to collect the displaced water - Place the irregular solid in the Eureka can and water will be displaced and collected. - The collected volume is the volume of the solid.

3 Force You need to know that force is: - A quantity that changes the motion, size, or the shape of a body. - A force is like a push or a pull. - A pulling force applied on a rubber band can change its shape. - A pushing force applied on a rubber ball can change its size. - A pushing force on cart can change its motion - Change in motion includes - Acceleration & deceleration - Changing direction - There are many types of forces, including - Frictional force - Magnetic force - Gravitational force - Force is measured in newtons (N) - 1N is the amount of force required to accelerate a mass of 1kg at a rate of 1m/s 2 - Meaning that Force = mass x acceleration (F = ma) - This is Newton s Second Law of Motion You need to know the interaction between multiple forces. - Force is a vector quantity. This means it has a direction and a magnitude. - This means multiple forces of multiple directions and magnitude can act on a object at the same time. - All the forces can be simplified or added up into one single force called the resultant force. - For example, a 5N force to the right and a 7N force to the left is acting on an object. - Forces acting in opposite directions cancel out - And since the magnitudes are not equal (7N - 5N = 2N) and the force to the left is stronger - The resultant force is 2N to the left. - If the opposite forces were equal in magnitude, they would completely cancel each other out. - There is no resultant force. - - The state of no resultant force, and hence no change in motion, is called equilibrium

4 You need to know what happens in systems of equilibrium - If a system is at equilibrium, there is no resultant force, and no change in motion. There are two possible situations: 1. Object is stationary - Stationary means no movement, so there is no change in motion - Imagine a box sitting on a surface. - The mass is affected by gravity and produces a weight force downwards. - Since the box is stationary, the weight must be balanced by an equal and opposite force. - This force is from the normal contact force - It comes from the contact between the box and the surface. - It is always equal and opposite of the force acting towards the surface 2. Object is at constant velocity - Constant velocity means that the motion is constant - so there still is no change in motion - Only acceleration or a change in direction is change in motion. - For example, a car moving at a constant speed to the right. - There are many forces acting on the car: - Driving force from the engine, friction, air resistance, normal force, gravitational force. - The car is not accelerating moving up or down, so the vertical forces must be balanced. - The car is also not accelerating or decelerating, so the horizontal forces must also be balanced. - Normal contact force = gravitational force - Friction + air resistance = driving force

5 You need to know what happens in systems not in equilibrium (accelerating objects) If the system is not in equilibrium, there is a resultant force, meaning there is change in motion - There is acceleration. Using Newton s Second Law of Motion, we can calculate the accelerations and forces of objects. - Force = mass x acceleration - F = m x a - N (kgm/s 2 ) = kg x m/s 2-1N is equal to 1 kgm/s 2. - Meaning it is important that mass is used in kilograms, not in grams. In situations with a resultant force, there is acceleration in the direction of the resultant force. - Take a box with mass 10kg. If a force of 50N was applied to the right, the resulting change in motion is: - F = ma : 50N / 10kg = 5m/s 2 to the right - Or take the same box from the equilibrium from the previous example. - If the surface was removed, the normal contact force would be removed - This object is now in freefall - There is only the weight of the object acting, pulling the object downwards. - (air resistance is ignored for simple models) - Using F = ma, 100N / 10kg = 10m/s 2 downwards. - This should be obvious, because on Earth, the acceleration due to gravity in freefall is 10m/s 2.

6 Hooke s Law You need to know the relationship between force and extension If you attach a mass (load) to a spring, it will stretch and extend. If we experimentally measure and record the - Mass of the load (hence the weight in N downwards) - The extension of the spring from its original length, We can calculate the relationship between the mass (force) and the resulting extension of the spring. Experiment: 1. Set up the apparatus as shown 2. Measure the unstretched length of the spring 3. Measure the mass m of the load and record in the table. - Find the force of the weight F, ( m (in kg) x 10 ) 4. Attach the mass to the spring and measure the total length l 5. Subtract original length from the new length to calculate the extension x of the spring. 6. Repeat steps 3 to 5 with different masses. From the data, we can see that there is a directly proportional relationship between force F, and extension x. - This relationship is called the Hooke s Law, and can be written as a formula: - Force = constant x extension - F = k x x - The constant k shows how much the force is required per unit extension. ( measured in N/m or N/cm) - Higher the spring constant, the harder it is to stretch. - e.g. a spring with a constant 5N/cm will require 5 newtons of force to stretch it by 1cm. - And a spring with constant 0.1N/cm only required 0.1 newtons of force to stretch it by 1cm. - Looking at the graph, the spring constant can be found by finding the the gradient - To find the gradient, we find rise/run, which is force / extension - F / x = k (Hooke s Law formula) - So this means steeper the gradient ( k ), the the spring constant increases (stiffer spring) - Meaning graphs with steeper gradients have springs that have higher spring constants.

7 You need to know behaviour of springs in parallel and series. If we repeated the experiment with two springs, we have two possibilities of the setup. 1. With two springs connected end-to-end ( in series ) 2. With two springs side-by-side ( in parallel ) As you can see from the diagram, the results are different to each other, and to the experiment with one spring. Force F / N Extension with 1 spring /cm Extension with 2 springs in series /cm Extension with 2 springs in parallel /cm Spring constant k: 2 N/cm 4 N/cm 1 N/cm Looking at the data, we can see how the new spring constant changes. - For comparison, we will take the situation with single spring, with the following notation for clarification: - F o = k o x x o (the subscript o meaning original) Springs in series (derivation of new spring constant): - Each of the spring is affected by the same force F o, and each obey Hooke s Law separately. - With each spring having the spring constant k o (same as a single spring) - This means each spring will have the extension x o. - If there are two springs, the total extension will be x o + x o, if there are three, x o + x o + x o. - This means the total extension will be nx o, where n is the number of springs in series. - If we considered the two springs as a whole, the equation becomes F o = k e x 2x o - Where k e is the new effective spring constant - (This is if we considered the multiple springs as single combined spring) - So we can say the effective spring constan t - k e = k o / n (where n is the number of springs) - The spring constant is divided by the number of springs - Hence the spring constant decreases - If there are 5 springs, the effective spring constant is k/5, giving total extension 5x. Springs in parallel (derivation of new spring constant): - The springs are side by side, so they share the force F o equally. - If the force was 10N, with two springs, each of the springs would be affected by a force of 5N. - This means the effective force on a single spring will be F o /n (where n is the number of springs) - Again, each spring obeys Hooke s law separately, so the extension will now be - F o /n = k o x x n. Where x n is the new extension caused by the new force, F o /n - This is rearranged to F o / k o = n x x n. And we know from the original equation - F o / k o = x o. So, we can say: n x x n = x o, which can be rearranged again to: - x n = x o / n, giving us the equation for the new extension for a single spring - So for two parallel springs, the extension will be x o /2, for each spring - But since they are next to each other, the total extension is also x o /2. - From this we can find the effective spring constant - F o = k e x x o /n, which rearranges to n x ( F o / k o ) = k e which is equal to: - k e = n x k o (where n is the number of springs) - The spring constant is multiplied by the number of springs - Hence the spring constant increases

8 You need to know what a limit of proportionality of extension-force graph is The limit of proportionality is the point on a extension-force graph where - Past the point, the material stops obeying Hooke s Law. - Meaning: the extension is no longer proportional to force. - The gradient will not be a straight line - This is because the material is ruined. - For example, a spring might be overstretched Pressure You need to know what pressure is and how to calculate it. - Pressure is force per unit area - Pressure = force area of contact - P = F A - Force is measured in newtons (N), and area is measured in metre squared (m 2 ) - Meaning the unit for pressure is newtons per metre squared, N/m 2-1 N/m 2 is also known as 1 Pa (pascals), which is the common unit of pressure. - If a force is applied to a surface, there is pressure exerted on the surface. - e.g. A 1x1x1 metre cube of mass 20kg is sitting on a table. What is the pressure exerted by the cube? - First find the force, so mass x gravity = force ( 20 x 10 = 200N ) - Then find the area of contact, which is the bottom side of the cube (1m x 1m = 1m 2 ) - Pressure is P = F/A, 200/1 = 200N/m 2 - Which is 200Pa. The box exerts a pressure of 200Pa on the table.

9 The syllabus says you should be able to, (SO check if you can): - Be able to distinguish between the mass and weight of an object. - Know that the Earth is the source of a gravitational field. - Demonstrate understanding that mass is a property that resists change in motion. - Describe, and use the concept of, weight as the effect of a gravitational field on a mass. - Describe an experiment to determine the density of a liquid and of a regularly shaped solid, and make the necessary calculation using the equation: - density = mass / volume or d = m / V - Describe the determination of the density of an irregularly shaped solid by the method of displacement, and make the necessary calculation. - Know that a force is measured in newtons (N). - Describe how forces may change the size, shape and motion of a body. - Find the resultant of two or more forces acting along the same line. - Explain how a system is in equilibrium when there is no resultant force. - Interpret extension-load graphs. - Plot extension-load graphs and describe the associated experimental procedure. - State and use Hooke s Law and recall and use the expression: - force = constant extension (F = kx) - Recognise the significance of the term limit of proportionality for an extension-load graph. - Recall and use the relation between force, mass and acceleration (including the direction): F = ma - Relate (without calculation) pressure to force and area. - Recall and use the equation P = F /A