Page 1 Chapter 10 Gravitation Some common Observations: 1. Newton observed an apple falling downwards from a tree. 2. Everything that is thrown upward always falls back towards the Earth. 3. The moon revolves around the Earth. 4. All the planets revolve around the sun All these observations can be explained by gravitational force. Gravitational force – A force of attraction between all the objects of the universe by virtue of their mass is called gravitational force. Kepler’s laws that helped in deriving equation of gravitational force: 1. The planets revolve around the Sun forming an eclipse with sun at its center. 2. The line joining the Sun and the Planets sweeps equal area in equal interval of time. 3. The ratio of the cube of average distance of a planet from the sun to the square of time taken to complete the orbit is always constant. i.e. r 3 /T 2 = constant where r = average distance of a planet from Sun and T = time taken by a planet to complete one revolution. Universal law of gravitation 1. Universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses That is, The gravitational force between two objects P and Q whose masses are ‘M’ and ‘m’ respectively and separated by a distance ‘d’ will be: F a M*m (a) 2. Universal law of gravitation also states that the gravitational is inversely proportional to the square of distance between them Therefore, F a 1/d 2 (b) Combining equation (a) and (b) F a M*m d 2 To replace the sign of ‘proportionality’ with ‘equals to’, a constant ‘G’ is used The value of ‘G’ was found to be 6.67*10 11 Nm 2 kg 2 Page 2 Chapter 10 Gravitation Some common Observations: 1. Newton observed an apple falling downwards from a tree. 2. Everything that is thrown upward always falls back towards the Earth. 3. The moon revolves around the Earth. 4. All the planets revolve around the sun All these observations can be explained by gravitational force. Gravitational force – A force of attraction between all the objects of the universe by virtue of their mass is called gravitational force. Kepler’s laws that helped in deriving equation of gravitational force: 1. The planets revolve around the Sun forming an eclipse with sun at its center. 2. The line joining the Sun and the Planets sweeps equal area in equal interval of time. 3. The ratio of the cube of average distance of a planet from the sun to the square of time taken to complete the orbit is always constant. i.e. r 3 /T 2 = constant where r = average distance of a planet from Sun and T = time taken by a planet to complete one revolution. Universal law of gravitation 1. Universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses That is, The gravitational force between two objects P and Q whose masses are ‘M’ and ‘m’ respectively and separated by a distance ‘d’ will be: F a M*m (a) 2. Universal law of gravitation also states that the gravitational is inversely proportional to the square of distance between them Therefore, F a 1/d 2 (b) Combining equation (a) and (b) F a M*m d 2 To replace the sign of ‘proportionality’ with ‘equals to’, a constant ‘G’ is used The value of ‘G’ was found to be 6.67*10 11 Nm 2 kg 2 Importance of Universal laws of gravitation: a. It explains the motion of planets around the Sun b. It explains the occurrence of tides due to Sun and moon c. It explains the force that binds us to the Earth. Free Fall When an object falls towards the Earth or grounds only due to gravitational without the application of any other force it is said to be in free fall. Acceleration due to gravitation: Since gravitation is force, any object that falls due to gravitational force undergoes acceleration: According to second law of motion F = m*a Where ‘m’ is the mass of the object and ‘a’ is the acceleration caused during motion If we consider the acceleration or ‘a’ caused due to gravity to be ‘g’ F = m*g (c) But we know that gravitational force = GMm (d) d 2 Combining equation (c) and (d) mg = GMm d 2 g = GM d 2 The distance is always taken from the center of the object. So when we consider an object falling on the surface of the Earth the distance will be the radius of the Earth or ‘R’ So, g = GM/R 2 Where, g = Acceleration due to gravity M = mass of Earth R = Radius of Earth. Page 3 Chapter 10 Gravitation Some common Observations: 1. Newton observed an apple falling downwards from a tree. 2. Everything that is thrown upward always falls back towards the Earth. 3. The moon revolves around the Earth. 4. All the planets revolve around the sun All these observations can be explained by gravitational force. Gravitational force – A force of attraction between all the objects of the universe by virtue of their mass is called gravitational force. Kepler’s laws that helped in deriving equation of gravitational force: 1. The planets revolve around the Sun forming an eclipse with sun at its center. 2. The line joining the Sun and the Planets sweeps equal area in equal interval of time. 3. The ratio of the cube of average distance of a planet from the sun to the square of time taken to complete the orbit is always constant. i.e. r 3 /T 2 = constant where r = average distance of a planet from Sun and T = time taken by a planet to complete one revolution. Universal law of gravitation 1. Universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses That is, The gravitational force between two objects P and Q whose masses are ‘M’ and ‘m’ respectively and separated by a distance ‘d’ will be: F a M*m (a) 2. Universal law of gravitation also states that the gravitational is inversely proportional to the square of distance between them Therefore, F a 1/d 2 (b) Combining equation (a) and (b) F a M*m d 2 To replace the sign of ‘proportionality’ with ‘equals to’, a constant ‘G’ is used The value of ‘G’ was found to be 6.67*10 11 Nm 2 kg 2 Importance of Universal laws of gravitation: a. It explains the motion of planets around the Sun b. It explains the occurrence of tides due to Sun and moon c. It explains the force that binds us to the Earth. Free Fall When an object falls towards the Earth or grounds only due to gravitational without the application of any other force it is said to be in free fall. Acceleration due to gravitation: Since gravitation is force, any object that falls due to gravitational force undergoes acceleration: According to second law of motion F = m*a Where ‘m’ is the mass of the object and ‘a’ is the acceleration caused during motion If we consider the acceleration or ‘a’ caused due to gravity to be ‘g’ F = m*g (c) But we know that gravitational force = GMm (d) d 2 Combining equation (c) and (d) mg = GMm d 2 g = GM d 2 The distance is always taken from the center of the object. So when we consider an object falling on the surface of the Earth the distance will be the radius of the Earth or ‘R’ So, g = GM/R 2 Where, g = Acceleration due to gravity M = mass of Earth R = Radius of Earth. Value of ‘g’ on Earth Mass of Earth = 6*10 24 kg Radius of Earth = 6.4*10 6 m G = 6.67*10 11 Nm 2 kg 2 g = 6.67*10 11 Nm 2 kg 2 * 6*10 24 kg (6.4*10 6 m) 2 = 9.8ms 2 Motion of objects due to gravity: The three equation of motion can be used with respect to gravity as well. Only the acceleration ‘a’ is replaced by acceleration due to gravity i.e. ‘g’ 1. v = u + at 2. s = ut + ½ at 2 3. 2as = v 2 – u 2 For motion due to gravitation the equations are transformed as follows: 1. v = u + gt 2. s = ut + ½ gt 2 3. 2gs = v 2 – u 2 Mass and Weight ? Mass is the total amount of matter present inside a substance. Mass does not change with place ? Weight is the force acting on a substance due to gravity that attracts it towards the Earth or the planet on which it is present. Weight can change from one place to another depending upon the gravitational force at that place. If mass of an object is ‘m’ Its weight = F = mg Or Weight = F = GMm d 2 Where ‘g’ is the acceleration caused due to gravity. For Earth the value of ‘g’ is 9.8ms 2 Weight of an object on moon Celestial body Mass (kg) Radius (m) Earth 5.98*10 24 6.37*10 6 Moon 7.36*10 22 1.74*10 6 Page 4 Chapter 10 Gravitation Some common Observations: 1. Newton observed an apple falling downwards from a tree. 2. Everything that is thrown upward always falls back towards the Earth. 3. The moon revolves around the Earth. 4. All the planets revolve around the sun All these observations can be explained by gravitational force. Gravitational force – A force of attraction between all the objects of the universe by virtue of their mass is called gravitational force. Kepler’s laws that helped in deriving equation of gravitational force: 1. The planets revolve around the Sun forming an eclipse with sun at its center. 2. The line joining the Sun and the Planets sweeps equal area in equal interval of time. 3. The ratio of the cube of average distance of a planet from the sun to the square of time taken to complete the orbit is always constant. i.e. r 3 /T 2 = constant where r = average distance of a planet from Sun and T = time taken by a planet to complete one revolution. Universal law of gravitation 1. Universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses That is, The gravitational force between two objects P and Q whose masses are ‘M’ and ‘m’ respectively and separated by a distance ‘d’ will be: F a M*m (a) 2. Universal law of gravitation also states that the gravitational is inversely proportional to the square of distance between them Therefore, F a 1/d 2 (b) Combining equation (a) and (b) F a M*m d 2 To replace the sign of ‘proportionality’ with ‘equals to’, a constant ‘G’ is used The value of ‘G’ was found to be 6.67*10 11 Nm 2 kg 2 Importance of Universal laws of gravitation: a. It explains the motion of planets around the Sun b. It explains the occurrence of tides due to Sun and moon c. It explains the force that binds us to the Earth. Free Fall When an object falls towards the Earth or grounds only due to gravitational without the application of any other force it is said to be in free fall. Acceleration due to gravitation: Since gravitation is force, any object that falls due to gravitational force undergoes acceleration: According to second law of motion F = m*a Where ‘m’ is the mass of the object and ‘a’ is the acceleration caused during motion If we consider the acceleration or ‘a’ caused due to gravity to be ‘g’ F = m*g (c) But we know that gravitational force = GMm (d) d 2 Combining equation (c) and (d) mg = GMm d 2 g = GM d 2 The distance is always taken from the center of the object. So when we consider an object falling on the surface of the Earth the distance will be the radius of the Earth or ‘R’ So, g = GM/R 2 Where, g = Acceleration due to gravity M = mass of Earth R = Radius of Earth. Value of ‘g’ on Earth Mass of Earth = 6*10 24 kg Radius of Earth = 6.4*10 6 m G = 6.67*10 11 Nm 2 kg 2 g = 6.67*10 11 Nm 2 kg 2 * 6*10 24 kg (6.4*10 6 m) 2 = 9.8ms 2 Motion of objects due to gravity: The three equation of motion can be used with respect to gravity as well. Only the acceleration ‘a’ is replaced by acceleration due to gravity i.e. ‘g’ 1. v = u + at 2. s = ut + ½ at 2 3. 2as = v 2 – u 2 For motion due to gravitation the equations are transformed as follows: 1. v = u + gt 2. s = ut + ½ gt 2 3. 2gs = v 2 – u 2 Mass and Weight ? Mass is the total amount of matter present inside a substance. Mass does not change with place ? Weight is the force acting on a substance due to gravity that attracts it towards the Earth or the planet on which it is present. Weight can change from one place to another depending upon the gravitational force at that place. If mass of an object is ‘m’ Its weight = F = mg Or Weight = F = GMm d 2 Where ‘g’ is the acceleration caused due to gravity. For Earth the value of ‘g’ is 9.8ms 2 Weight of an object on moon Celestial body Mass (kg) Radius (m) Earth 5.98*10 24 6.37*10 6 Moon 7.36*10 22 1.74*10 6 Weight of an object on moon can be given by: Wm = GMmm (p) (Mm = mass of moon; m = mass of object; R m= radius of moon) R 2 m Weight of object on Earth can be given by: We = GMem (q) (Me = mass of Earth; m = mass of object; Re= radius of Earth) R 2 e ? Wm = GMmm * R 2 e {Dividing equation (p) by equation (q)} We R 2 m * GMem ? Wm = Mm * R 2 e We R 2 m * Me ? Wm = 7.36*10 22 * (6.37*10 6 ) 2 We (1.74*10 6 ) 2 * 5.98*10 24 ? Wm = 0.165 or 1 We 6 Hence, the weight of an object on moon is 1/6 of its weight on Earth. Thrust or force and Pressure ? Thrust – The force acting on an object perpendicular to its surface is known as thrust If a block of wood is pushed downward than Force or thrust is same Thrust Movement of block On an inclined surface some part of the force due to weight of the object is acting horizontally towards inclination, hence thrust is less than the force. Thrust is only that part of the force which acts perpendicular to the surface. Page 5 Chapter 10 Gravitation Some common Observations: 1. Newton observed an apple falling downwards from a tree. 2. Everything that is thrown upward always falls back towards the Earth. 3. The moon revolves around the Earth. 4. All the planets revolve around the sun All these observations can be explained by gravitational force. Gravitational force – A force of attraction between all the objects of the universe by virtue of their mass is called gravitational force. Kepler’s laws that helped in deriving equation of gravitational force: 1. The planets revolve around the Sun forming an eclipse with sun at its center. 2. The line joining the Sun and the Planets sweeps equal area in equal interval of time. 3. The ratio of the cube of average distance of a planet from the sun to the square of time taken to complete the orbit is always constant. i.e. r 3 /T 2 = constant where r = average distance of a planet from Sun and T = time taken by a planet to complete one revolution. Universal law of gravitation 1. Universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses That is, The gravitational force between two objects P and Q whose masses are ‘M’ and ‘m’ respectively and separated by a distance ‘d’ will be: F a M*m (a) 2. Universal law of gravitation also states that the gravitational is inversely proportional to the square of distance between them Therefore, F a 1/d 2 (b) Combining equation (a) and (b) F a M*m d 2 To replace the sign of ‘proportionality’ with ‘equals to’, a constant ‘G’ is used The value of ‘G’ was found to be 6.67*10 11 Nm 2 kg 2 Importance of Universal laws of gravitation: a. It explains the motion of planets around the Sun b. It explains the occurrence of tides due to Sun and moon c. It explains the force that binds us to the Earth. Free Fall When an object falls towards the Earth or grounds only due to gravitational without the application of any other force it is said to be in free fall. Acceleration due to gravitation: Since gravitation is force, any object that falls due to gravitational force undergoes acceleration: According to second law of motion F = m*a Where ‘m’ is the mass of the object and ‘a’ is the acceleration caused during motion If we consider the acceleration or ‘a’ caused due to gravity to be ‘g’ F = m*g (c) But we know that gravitational force = GMm (d) d 2 Combining equation (c) and (d) mg = GMm d 2 g = GM d 2 The distance is always taken from the center of the object. So when we consider an object falling on the surface of the Earth the distance will be the radius of the Earth or ‘R’ So, g = GM/R 2 Where, g = Acceleration due to gravity M = mass of Earth R = Radius of Earth. Value of ‘g’ on Earth Mass of Earth = 6*10 24 kg Radius of Earth = 6.4*10 6 m G = 6.67*10 11 Nm 2 kg 2 g = 6.67*10 11 Nm 2 kg 2 * 6*10 24 kg (6.4*10 6 m) 2 = 9.8ms 2 Motion of objects due to gravity: The three equation of motion can be used with respect to gravity as well. Only the acceleration ‘a’ is replaced by acceleration due to gravity i.e. ‘g’ 1. v = u + at 2. s = ut + ½ at 2 3. 2as = v 2 – u 2 For motion due to gravitation the equations are transformed as follows: 1. v = u + gt 2. s = ut + ½ gt 2 3. 2gs = v 2 – u 2 Mass and Weight ? Mass is the total amount of matter present inside a substance. Mass does not change with place ? Weight is the force acting on a substance due to gravity that attracts it towards the Earth or the planet on which it is present. Weight can change from one place to another depending upon the gravitational force at that place. If mass of an object is ‘m’ Its weight = F = mg Or Weight = F = GMm d 2 Where ‘g’ is the acceleration caused due to gravity. For Earth the value of ‘g’ is 9.8ms 2 Weight of an object on moon Celestial body Mass (kg) Radius (m) Earth 5.98*10 24 6.37*10 6 Moon 7.36*10 22 1.74*10 6 Weight of an object on moon can be given by: Wm = GMmm (p) (Mm = mass of moon; m = mass of object; R m= radius of moon) R 2 m Weight of object on Earth can be given by: We = GMem (q) (Me = mass of Earth; m = mass of object; Re= radius of Earth) R 2 e ? Wm = GMmm * R 2 e {Dividing equation (p) by equation (q)} We R 2 m * GMem ? Wm = Mm * R 2 e We R 2 m * Me ? Wm = 7.36*10 22 * (6.37*10 6 ) 2 We (1.74*10 6 ) 2 * 5.98*10 24 ? Wm = 0.165 or 1 We 6 Hence, the weight of an object on moon is 1/6 of its weight on Earth. Thrust or force and Pressure ? Thrust – The force acting on an object perpendicular to its surface is known as thrust If a block of wood is pushed downward than Force or thrust is same Thrust Movement of block On an inclined surface some part of the force due to weight of the object is acting horizontally towards inclination, hence thrust is less than the force. Thrust is only that part of the force which acts perpendicular to the surface. ? Pressure is the force or thrust applied per unit area Pressure = Thrust Area The units of pressure are Nm 2 or Pascal (P) ? It is recommended to use flat shoes while walking on snow or sand because they have higher surface area and hence less pressure is applied while walking. ? It is easy to hammer pointed nails on a wall because it has less surface area an apply high pressure on the wall. Buoyancy The ability of an object to float on the surface of a liquid is called buoyancy. The upward force exerted by the water or liquid on the object that keeps it floating is called buoyancy force. 1. Gravitation pulls an object downward when it is kept in water. However, water also applies an upward force on the object. If the gravitational force is higher than the upward force applied by water the object sinks but if the force applied by water is higher than the gravitational force it floats. 2. Other reason is the density of the object and that of liquid in which it is placed. The objects that have density higher than the liquid in which they are placed sinks while, Those with densities lower than the liquids float on its surface. Archimedes’ Principle When an object is immersed fully or partially in water, it experiences an upward force which is equal to the weight of the water displaced by it. Upward force, also known as the force of buoyancy. Applications of Archimedes’ principle: 1. Designing the ships 2. Designing submarines 3. Determine the purity of milk 4. Make hydrometers used to determine the density of liquids. Relative density Relative density is defined as the density of a substance with respect to water. Relative density = Density of the object Density of waterRead More
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