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Saturday, July 3, 2010 @ 10:47 PM Worksheet 1. When solid A of mass 2 g is immersed in a measuring cylinder filled with water, it displaces a volume of 4cm³. What is the density of the solid A? A. 0.5 g cm-³ B. 2 g cm-³ C. 5 N cm-³ D. 20 N cm-³ 2. A bottle full of water has a mass of 200g. When the same bottle is filled with liquid X, the mass becomes 180g. If the mass of the empty bottle is 100g, what is the density of liquid X? ( Take the density of water as 1.0g cm -³) A. 0.2g cm-³ B. 0.8g cm-³ C. 0.9g cm-³ D. 1.2g cm-³ 3. A wooden block of dimension 1 m X 1 m X 1 m has a mass of 800kg. A jar attached a steel plate of dimension 1 m X 1 m X 0.02 m to the block. Given that the steel plate has a mass of 140kg, what is the density of the combination? A. 800kg m-³ B. 922kg m-³ C. 3900kg m-³ D. 7000kg m-³ 4. A 100kg rock it being hung freely on the Moon. When an astronaut pushes the rock upwards, he will feel that A. the rock us easier to be pushed than on Earth. B. the rock is more difficult to be pushed as it is on Earth. C. the rock requires as much effort to be pushed as on Earth. D. the rock requires no effort to be pushed. 5. An astronaut in space wants to compare the mass of two balls. He holds the two balls in each of his hands and moves both hands up and down slightly for a few times. What is the reason for doing so? A. He is trying to compare the inertia of two balls. The one with a higher mass tends to be more difficult to be moved and to be stopped. B. He is trying to compare the weight of the two balls. The one with a higher mass tends to be easier to be moved and to be stopped. C. He is trying to compare the weight of the two balls. The one with a higher weight tends to be more difficult to be moved and to be stopped. D. He is trying to compare the weight of the two balls. The one with a higher weight tends to be easier to be moved and to be stopped. 6. Which if the following is true ( assuming the effect of air resistance is negligible) ? A. The period of oscillation of a pendulum is longer on the Earth than on the Moon. B. An object being thrown upwards on the Moon will reach the same height as when it is being thrown upwards in the Earth. C. A ball thrown horizontally on the Moon will travel the same horizontal distance as when it is being thrown horizontally on the Earth. D. A stone thrown upwards on the Moon will have the same maximum gravitational potential energy as when is it being thrown upwards on the Earth. 7. A rectangular metal block had a dimension of 5cm x 3 cm x 2cm. If the density of the metal is 8000 kgm³, find the mass of the block. 8. (a) A small container has a mass of 100g. When it is completely filled with water, it weighs 4N. If the density of water is 1000kgm³, find the capacity of the container. [The force of gravity acting on a mass of 1 kg is 10N.] (b) The container is then emptied and completely filled with another liquid of density 850 kgm³. What is its weight now? 9. The weight of an insoluble object is 3.0N in air. It is placed into a measuring cylinder filled with some water. The amount of water displaced is 60 cm³. Determine the density of the object. [ The force of gravity acting on mass of 1kg is 10N ] 10. A piece of uniform copper wire 10m long had a mass of 0.35kg. If the density of copper is 8900 kgm³, determine the diameter of the wire. 11. Five coins have a mass of 50g each. When the coins were put into a measuring cylinder containing water, the level of the water rose from 24 cm³ to 48 cm³. (a) Find the volume of one coin . 12. If 100 cm³ of water is mixed with 300 cm³ of a liquid to form a mixture of density 850 kgm³. Find the density of the liquid , assuming that there is no contraction in volume .[Density of water = 1000 kgm³ ]
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Wednesday, June 30, 2010 @ 5:47 AM  Content
Let's explore ! Mass and weight When we say that a person weighs 100kg , we actually mean that the person had a body mass of 100kg . When we buy a 5kg bag of rice , we actually mean the mass of the bag of rice is 5kg and not the weight . In Physics , weight and mass are two very different quantities . In everyday language , we often misuse the term weight when we mean mass . So what is the difference between mass and weight ? What is mass ? Mass is a measure of the amount of matter or substance in a body . It is a property of a body that cannot be changed by its location , shape and speed . The amount of mass body has depends on the number and composition of atoms and molecules that make up the body . The SI unit for mass is the kilogram (kg) . Large masses (e.g truck ) are usually measured in tonnes while small masses (e.g pencil ) are usually measured in grams .  When we say a person weighs more than another , we are comparing the Earth's gravitational force acting on each person . The weighing scale is simply an instrument that allows us to measure and compare who had more gravitational force acting on her . So , shouldn't weighing scales reflect newtons and not kilograms then ? Are our common weighing scales wrong ? You will find out later . What is weight ? Have you ever wondered why objects fall to the ground after you throw them up in the air ? Well , it is due to a force called weight which pulls them back down to Earth . This force is the result of the gravitational pull exerted by the Earth . Weight is a force and had direction . The direction is downward - towards the centre of the Earth . Since weight is a force , its SI unit is newton (N) , not kilogram (kg) . This force is also called gravitational force or gravity . What is a gravitational field ? The Earth 's gravity is experienced by any object near it . The region surrounding the Earth where gravity is experienced is called the gravitational field .The force experienced is the strongest on the surface of the earth and gets weaker further away .  Earth is surrounded by a gravitational field . Field lines are drawn to represent the gravitational field . What is gravitational field strength ? The weight of an object depends on the strength of the gravitational pull . For example , an object weighs much less on the moon than on Earth . This is because the Moon's gravitational pull is much less than the Earth's . The mass of the object , however , stays the same whether on Earth or on the Moon . Gravitational field strength g is defined as the gravitational force acting per unit about 10kg-1 . This means that a 1kg mass experiences a force of 10N due to Earth's gravitational pull. On the other hand , the same 1 kg mass on the Moon experiences a gravitational force of only 1.6N . Hence , we say that the gravitational field strength on the Moon us 1.6N kg-1 .  The sun is an extremely massive star . All planets of the solar system , including Earth , are held in orbits due to the Sun's gravitational pull . How are mass and weight related ? The weight or amount of gravitational force acting on an object is dependent in its mass . The more mass an object has , the greater the gravitational force acting on it . Forces that F=ma . Since weight is gravitational force , from this equation , we can see that weight is directly proportional to the mass of a body . In kinematics , all objects falling freely accelerate at the rate of 10 m/s2 . This acceleration is the same as the Earth's gravitational field strength , which we will denote as g too . Therefore we can write : W=mg where W= weight ( in N ) M= mass of object ( in kg ) and G= gravitational field strength ( in Nkg-1) Worked Example 1 A mobile phone has a mass of 75g . Find its weight if g is 10 Nkg-1. Solution Mass if mobile phone = 75g = 75 x 0.001 kg = 0.075kg Weight of mobile phone = mass of mobile phone x g = 0.075 kg x 10 N kg-1 = 0.75 N  Most common laboratory instruments for measuring mass actually measure weight , but are calibrated to give the readings in mass . What do common weighing instruments measure ? Common weighing instruments like the electronic balance , spring balance and the bathroom scales actually measure the weight of an object , and not its mass . These machines , however , are calibrated to give readings in grams (g) or kilograms (kg) . This means that an object will have different mass readings for different gravitational field strengths . For example , if an astronaut steps on a bathroom scale on the Moon , the reading will be lower than that taken on Earth . This is because the gravitational field strength on the Moon , 1.6 N kg-1 , is less . From this , we can see that a weighing scale calibrated for use on Earth cannot be used on the Moon . A different weighing scale calibrated to suit the Moon's gravitational field strength will have to be used . This weighing scale will then give accurate mass measurements on the Moon . How is mass measured ? To avoid the hassle of using different weighing scales for different gravitational field strengths , the mass of an object can be measured easily using the beam balance . The beam balance compares the gravitational force acting on an object with standard masses . As both pans of the beam balance experience the same gravitational field strength , the mass readings taken for an object whether on Earth or the Moon will be the same .  The spring balance is usually calibrated to give readings to both newtons (N) and grams (g) . It works by giving a reading proportional to the extension of the spring caused by the weight of the object . Thus the greater the gravitational pull , the greater the extension of the spring . Mass and Weight Comparison
Below is a video of mass & weight The acceleration of free fall on the Moon is 1.6m/s 2 . The acceleration of free fall on Earth is 10m/s 2 . A rock has a mass of 10kg on Earth . Calculate the weight of the rock (a) on Earth ; (b) on the Moon . Solution We know that :
Weight of rock on the Moon = 10kg x 1.6 m/s 2= 16N Worked Example 3 A satellite is lanuched from Earth into orbit . Whst happens to the mass and weight of the satellite ? Solution The mass of the satellite remains the same . Since the gravitational field strength is lower in space than on the Earth's surface , its weight decreases . Inertia Imagine you are on a Safari in Africa . Being adventurous , you take the risk of walking in an open flat terrain . Suddenly , a big elephant comes charging you . Should you run away in a straight line or zigzag manner to escape from the charging elephant ? The answer may seem obvious , but what is the reasoning behind it ? In order to explain it properly , we need to understand inertia and how it is related to mass . What is inertia ? An object that has mass will have a reluctance to change its state of rest or motion . This property is known as inertia . Stated formally : Inertia of an object refers to the reluctance of the object to change its state of rest or motion . The inertia of an object depends on its mass . An object with more mass has greater inertia . In other words , the larger the mass of an object , the harder it is to start moving , slow down , move faster or change direction .  With this understanding , you will see that it is harder for an elephant to chase you in a zigzag manner . If the elephant tries to do that , it will probably trip and fall ! A reason that drivers wear seat belts for safety when driving is because of inertia . Without a seat belt , if the driver suddenly applies the brakes , he will continue to move forward due to his inertia and crash into the windscreen . With a seat belt , the driver will prevented from crashing into the windscreen . Density If you compare equal volumes of ice and lemon with your hands , you will feel that the ice is lighter than the slice of lemon . The reason ice floats while a lemon slice sinks in water is because ice and lemon have different densities compared to water . When we talk about density , we are in fact talking about how much mass is packed into given space . What is density ?  The density of a substance is defined as its mass per unit volume . For pure substances, it is a fixed property . For example , the density of pure gold is 19 300 kg m³ . If the density of a gold ring is not 19 300 kg m³ , then it is not made of pure gold - it must have some impurities in it . To calculate the density of a substance , we need to know its mass m and its volume V . Density ρ ( Greek alphabet "rho" pronounced as "row" ) is given by : ρ = m / V m = mass of object ( in kg )where ρ = density V = volume of object ( in m³) The SI unit of density is kilogram per cubic metre ( kg/m³). If mass is measured in kilograms (kg) and the volume in cubic metres (m³) , the unit of density would be the SI unit . However , if mass is measured in grams (g) and volume in cubic centimetres (cm³) , the unity of density would be gram per cubic centimetre or g/cm³ . As most objects we handle daily have much smaller masses and volumes , the common unit of density used is g/cm3 . Substances that float on water have lower densities than water . Similarly , substances that sink in water have higher densities than water. Thus we can conclude from the earlier example that lemon is denser than water , but ice is less dense than water . Below is a video of an example showing different densities of liquid substances . Why does a heavy steel ship float ? We know an iron ball sinks in water but a big ship bulit from tonnes of steel floats ! Why is this so ?  When an object like a cruise liner is made up of more than one material , we will have to consider its average density . Average density of an object is calculated by diving its total mass by its total volume . For example , a cruise liner has a mass of 76 800 tonnes . It also occupies a larger volume - 268m long , 32m wide and 13 storeys ( or 25m ) high . This volume is not entirely mafe up of steel - it contaisn a cosiderable amount of air in the various rooms and cabins . So , what is the average density of the ship ? Assuming a cuboidal shape , its volume is 268 x 32 x 25 = 214 400 m³ . Its mass is 76 800 tonnes = 76 800 x 1000kg . Therefore , the average density of the ship can be calculated : Average density = mass / volume = (76 800 x 1000 ) divide by 214 400 = 358 kg m³ . The average density of the ship is actually less than the density of water . Therefore , the ship of able to float . |