It covers many of the key math skills you will need as you progress through. Comment on the quality of the data and whether repeated results are equal within the limits.
FOCUS POINTS
The number of digits, called significant digits, given for a measurement indicates how accurate we think it is. If a number is expressed in standard notation, the number of significant figures is the number of figures to the power of ten.
Test yourself
Worked example
1 Calculate the volume of a rectangular box that is 30 cm long, 25 cm wide and 15 cm high in cubic metres. To measure a time interval in an experiment, you must first select a timer that is accurate enough for the task.
Practical work
To measure very short time intervals, a digital clock that can be triggered to start and stop by an electronic signal from a. A half-meter ruler has zero at the end of the ruler and can therefore be used without introducing a systematic error.
Going further
Motion
- Balanced and unbalanced forces
In Figure 1.2.3c the velocity increases with time and the acceleration of the object decreases. The mass of an object is the measure of the amount of matter in it.
Going further Practical work
Friction
Friction (drag) acts on an object, such as a vehicle or a falling leaf, moving through gas (air resistance) that opposes the object's motion. Drag increases as the speed of the object increases and acts to reduce acceleration and slow the object.
Circular motion
As the object accelerates, the air resistance opposing its motion increases as its speed increases. The resultant force on the object is then zero since the gravitational force balances the frictional force.
FOCUS POINT
Turning effect of forces
It depends on both the magnitude of the force and how far it acts from the pivot. It can also be said that the sum of the moments is zero when the body is in equilibrium.
Centre of gravity
The position of an object's center of gravity affects whether or not it will be stable when tilted. What can you say about the relationship between the extension of the spring and the stretching force.
Energy
Chemical energy stored in the battery is transferred by an electric current (electric drive) to kinetic energy in the electric motor. The weight is raised when the kinetic energy stored in the motor is transferred (by mechanical processing) to gravitational potential energy stored in the weight. As an object falls, its speed increases and it gains kinetic energy at the expense of its gravitational potential energy.
The energy of the bob is all the gravitational potential energy at the end of the swing and all the kinetic energy as it passes through its center position.
Work
Energy resources
The sun is the main source of energy for many of the energy sources described on the previous pages. The efficiency of a large installation can be as high as 85-90%, since many of the causes of losses in thermal power plants (e.g. water cooling towers) are absent. The contribution of the most important energy sources to the world's total energy consumption at present is given in table 1.7.2.
1 The efficiency of a device is the percentage of the energy supplied that is usefully transferred.
Power
In Figure 1.8.13a, atmospheric pressure is applied equally to each surface of the fluid and the levels are the same. The pressure of the liquid column BC is therefore equal to the extent to which the gas pressure exceeds atmospheric pressure. The difference in height between the top of the mercury column and the surface of the mercury in the bowl (Δh) is a measure of the atmospheric pressure in mm of mercury (mm Hg).
Atmospheric pressure produces a vertical force on the mercury surface, so Δh is the vertical height of the column;.
States of matter
Particle model
As the temperature of the gas increases, the average speed and kinetic energy of the particles also increase. Collisions with the surfaces of the container occur more often, and thus the gas pressure increases. This movement is caused by collisions between microscopic particles in suspension and particles of gas or liquid.
1 What are the specks of light in the glass cell of the Brownian motion experiment.
Gases and the absolute scale of temperature
If the volume of a solid mass of gas is halved by halving the volume of the container (Figure 2.1.8), the number of particles per cm3 be doubled. 6 Describe the effect on the pressure of a solid mass of gas if the volume is reduced, but the temperature of the gas is kept constant. Assuming the temperature remains constant, calculate the volume of the gas when the pressure is
According to the kinetic particle model (Topic 2.1.2), the particles of solids and liquids are in constant vibration.
Thermal expansion of solids, liquids and gases
The heat from the fire causes the bimetallic strip to bend and complete an electrical circuit, sounding the alarm (Figure 2.2.3a). The one in Figure 2.2.3b uses a bimetallic strip in an electric heating circuit, such as an iron. In Figure 2.2.1, the axle has been shrunk by cooling in liquid nitrogen at -196 °C until gears can be fitted onto it.
When heated, copper expands more than iron and to allow this, the strip is bent with the copper on the outside (Figure 2.2.2b).
Specific heat capacity
The increase in kinetic energy associated with this motion increases the internal energy of the object. When the average kinetic energy of the particles in both bodies is the same, they have the same temperature. 1 If 25,000 J of energy is supplied to a mass of 2 kg and the temperature rises from 10°C to 35°C, calculate the specific heat capacity of the mass.
If the resulting temperature of the mixture is 25°C, what is the specific heat capacity of the metal if that of water is 4200 J/(kg °C).
Melting, boiling and evaporation
When two substances at different temperatures are mixed, energy flows from the one with the higher temperature to the one with the lower temperature until both reach the same temperature - the temperature of the mixture. Similarly, when energy is applied to a boiling liquid, the temperature of the liquid does not change. By measuring the mass of water m produced when the energy ΔE is transferred to the melting ice, the specific latent heat of fusion for the ice can be calculated.
How much energy must be supplied to increase the temperature of 10 g of liquid from 20°C to 50°C.
Conduction
Most metals are good thermal conductors; materials such as wood, glass, cork, plastic and fabrics are thermal insulators (poor conductors). Bronze conducts thermal energy away from the paper quickly, preventing the paper from reaching the temperature at which it burns. Metal objects below body temperature feel colder than objects made of poor conductors—even if all the objects are exactly the same temperature—because metal objects dissipate heat energy faster from the hand.
There are many solids that have fewer free electrons available to transfer thermal energy than metals and thus are poorer thermal conductors than metals but better thermal conductors than insulators.
Convection
The direction of the convective current created by the candle is made visible by the smoke from the touch paper (made by soaking brown paper in a strong potassium nitrate solution and drying it). During the day, the temperature of the land rises faster than that of the sea (because the specific heat capacity of the land is much smaller; see Topic 2.2.2). The warm air above the land rises and is replaced by colder air from the sea.
The air above the sea is warmer than that over the land and a breeze blows from the land (Figure 2.3.6b).
Radiation
Short-wavelength light and infrared light from the sun penetrate the greenhouse glass and are absorbed by the soil, plants, etc., raising their temperature. In order for the average temperature of the Earth to remain unchanged, a balance must be achieved between the incoming radiation and the radiation emitted by the Earth's surface. If there is an accumulation of carbon dioxide and methane in the atmosphere, the balance between the incoming solar radiation and the average power emitted by the Earth will be disturbed.
The higher the surface temperature of the object above its surroundings, and the larger its surface area, the greater the amount of radiation it emits and the greater its cooling rate.
Consequences of thermal energy transfer
1 State the source of thermal energy when the temperature of the thermometer rises after it is removed from the ice. Thermal energy is transferred to the fluid by conduction as it passes over the engine block. When the liquid enters the radiator, thermal energy is transferred by conduction to the radiator, which then radiates energy in the infrared to the surroundings.
Thermal energy is radiated from burning wood or coal and heats objects in the room that absorb it.
Waves
- Reflection of light
- Refraction of light
- Thin lenses
- Dispersion of light
- rays
- rays are produced when high-speed electrons are stopped by a metal target in an ray tube. rays
- rays and gamma rays
- Electrical quantities
6 In Figure 3.2.19 at which of the points A to D will the observer see the image in the plane mirror of the object. Similarly, rays from the submerged part of the pencil in Figure 3.2.24 are refracted at the water surface. The number of compressions produced per second is the frequency f of the sound wave (and is equal to the frequency of the vibrating speaker cone).
If we take the speed of sound in air to be 340 m/s, calculate the frequency of the sound wave. Place the drawing compass at a point such as A (Figure 4.1.6b) near one pole of the magnet. Continue this process until you reach the other pole of the bar magnet (in Figure 4.1.6b this is the S pole).