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Kepler’s second law states that an imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals. GRADE 9 ADVANCED – EOT presentation • Kepler found that orbits might change due to gravitational effects from, or collisions with, other objects in the solar system. • He also found that the planets move faster when they are closer to the Sun and slower when they are farther away from the Sun. Term 3 - 2023-2024 GRAVITATIONAL FORCE • It is said that Isaac Newton watched an apple fall and this led to his theory of gravity. • He suggested that there was a force acting on the apple to make it fall. • He extended that idea to all objects, including our planet, the Moon and the Sun. He called it the gravitational force. Factors that affect gravity The effect of mass on gravity The effect of distance on gravity 1. Mass 2. Distance Follows inverse square law Law of Universal Gravitation 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 CHECKPOINT Relation between Kepler’s Third Law and Universal Law of Gravitation To calculate the orbital period of a satellite Write the final answer in days. GUIDED PRACTICE 𝑚 = 5.97 × 10 𝑘𝑔 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 𝑚 = 5.97 × 10 𝑘𝑔 𝑟 = 6 ⋅ 38 × 10 𝑚 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 𝑟 = 6 ⋅ 38 × 10 𝑚 An ellipse has two foci Kepler’s first law states that the paths of the planets are ellipses, with the Sun at one focus. Very Important DEFINING WORK 1 joule of work is done when a force of 1 N acts on a system over a displacement of 1 m . 1 J = 1 Nm NOTE : • Work is a scalar quantity. • Work is said to be done only if an objects moves in the same direction as the applied force . The distance from earth to the sun changes throughout a year . Work done by a constant force Work done = Force x Displacement W = F x d Refer to presentations used in class Module 10 –Lesson 1 – Work and energy – Part 3 to 6 PICTURE 1 FORCE : A force is being applied by the man on the wall. DISPLACEMENT : But there is no displacement happening . WORK : Since there is no displacement happening in the direction of applied force , no work is being done . PICTURE 2 FORCE : An upward force is being applied by the man on the box . DISPLACEMENT : The box will move in the upward direction . So, displacement occurred . WORK :Since there is displacement happening in the direction of applied force , work is being done . Types of work Positive work Positive work Force and displacement in same direction. Negative work Force and displacement in opposite direction. Zero work Zero work 1. Force applied , but zero displacement . 2. Force and displacement perpendicular to each other . Work done by Multiple forces on the box NOTE: When there are multiple forces acting on an object Total work done = Sum of work done by each force . RECALL Do you know how to find out the area of these shapes? The force displacement graph PARTNER TIME Find out the work done Work done on force displacement graphs CONSTANT FORCE CHANGING FORCE Work done by a constant or varying force = Area under the force displacement graph Work done by a constant or varying force = Area under the force displacement graph Work is calculated by interpreting the area of the rectangle in the graph Work is calculated by interpreting the area of the triangle in the graph Practice Find the total work done POWER (P) FORMULAS • The rate at which energy is transformed is power . • It is measured in watts (W). • 1 W = 1 J/s W = ΔE 1 Δ𝑘𝐸 = 𝑚 𝑣 − 𝑣 2 𝑃= 𝑤 𝑡 𝑃= 𝑃= 𝑃= 𝐹𝑑 𝑡 𝑚𝑔𝑑 𝑡 𝑤 𝑡 Challenge Practice problem 2 Kinetic Energy Energy due to motion NOTE Translational kinetic energy is proportional to the square of the object’s Speed. Translational Kinetic Energy Energy due to changing position 𝐾𝐸 = 1 𝑚𝑣 2 m – mass of object v - velocity of object Rotational Kinetic Energy Energy due to rotational motion 𝐾𝐸 = 1 𝐼𝜔 2 I – moment of inertia ω - angular velocity of object Guided Practice Gravitational Potential Energy ( GPE ) RECAP Work done by gravity (Wg) • Gravitational Potential Energy (GPE) is the stored energy due to gravity. GPE = m g h Where , h is the object’s distance above the reference level g is the gravitational field strength • Lifting an object : Wg = - mgh • Unit - joules (J) • Lowering an object : Wg = mgh The negative sign is because displacement is upwards and gravitational force acts downward . RECAP LAW OF CONSERVATION OF ENERGY The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. 𝐾𝐸 + 𝑃𝐸 = 𝐾𝐸 + 𝑃𝐸 Guided Practice 1 EXAMPLE Kinetic energy Change in kinetic energy Change in kinetic energy = Final KE – Initial KE Analyzing Bernoulli’s Principle BERNOULLI’S PRINCIPLE Refer to the textbook – Page 249 and 250 Bernoulli’s principle states that as the velocity of a fluid increases, the pressure exerted by that fluid decreases. Velocity increases Pressure decreases Ideal fluid Change in kinetic energy =Work done Work is proportional to force Applications of Bernoulli’s principle Enters through wider mouth of pipe with velocity v1 Kinetic energy increases Force is proportional to pressure Reaches narrower portion of pipe Velocity increases Net work is positive CONCLUSION : Relation between pressure and velocity Pressure at the input section , where velocity is lower, must be larger than the pressure at the output end , where velocity is higher. Difference between Pascal and Bernoulli’s Principles As you learned, both these principles define how fluids behave with pressure. Pascal showed that fluid pressure is the same for a given depth and that pressure change is transmitted equally everywhere. Paint sprayers Gasoline engine carburetors Bernoulli showed that pressure changes in a fluid when it is moving. Pascal's principle only applies to static fluids, that is, fluids at rest, whereas Bernoulli's principle only applies to fluids in motion. Application of Pascal’s Principle – Hydraulic Lift Force Exerted by a Hydraulic Lift the force exerted by the second is equal to the force exerted by the first piston multiplied by the ratio of the area of the second piston to the area of the first piston WARM-UP QUESTION Which law states that any change in pressure applied at any point on a confined fluid is transferred undiminished throughout the fluid? A Pascal’s principle C buoyancy principle D Archimedes’ principle CORRECT B Bernoulli’s principle WRITING Guided Practice CHECKPOINT Guided Practice CHALLENGE Guided Practice THE WORK – ENERGY THEOREM Kinetic energy The work-energy theorem states that the work done (W) on a system is equal to the change in energy (ΔE) of the system, W = ΔE Change in kinetic energy Model of work-energy theorem Change in kinetic energy = Final KE – Initial KE CHALLENGE HOMEWORK Law of Conservation of Energy • The law of conservation of energy states that in a closed, isolated system, energy can neither be created nor destroyed. • So, the total change of energy in any system is always equal to the total energy transferred into or out of the system CHALLENGE ! MECHANICAL ENERGY Imagine a system consisting of a 10 N ball falling to the earth. Find the mechanical energy of the system in all three cases . Example 1: Rollercoasters EXAMPLES OF CONSERVATION AND OTHER FORMS OF ENERGY CHECKPOINT ( LMS > Physics > Week 3 > Period 5> Checkpoint ) Example 2 : Skiing Example 2 : Skiing 1. At which point is the PE highest ? The roller-coaster car is nearly at rest at the top of the first hill, and the total mechanical energy in the Earth-roller coaster car system is the system's gravitational potential energy at that point. 2 .At which point is the KE the highest ? 3. At which points are the ME equal to each other? • When you ski down a steep slope, you begin from rest at the top of the slope and the total mechanical energy is equal to the gravitational potential energy. • Once you start skiing downhill, the gravitational potential energy is transformed to kinetic energy. • As you ski down the slope, your speed increases as more potential energy is transformed to kinetic energy. Example 3 : Pendulums Pendulums • The simple oscillation of a pendulum also demonstrates Conservation of mechanical energy. • The system is the pendulum bob and Earth. The reference level is chosen to be the height of the bob at the lowest point. When an external force pulls the bob to one side, the force does work that adds mechanical energy to the system. • At the instant the bob is released, all the energy is in the form of potential energy, but as the bob swings downward, potential energy is transformed to kinetic energy. When the bob is at the lowest point, the gravitational potential energy is zero, and the kinetic energy is equal to the total mechanical energy. EXAMPLE RECAP Guided Practice 1 LAW OF CONSERVATION OF ENERGY The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. 𝐾𝐸 + 𝑃𝐸 = 𝐾𝐸 + 𝑃𝐸 KEPLER’S LAWS Kepler’s first law Kepler’s second law states that the paths of the planets are ellipses, with the Sun at one focus. states that an imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals. The distance from earth to the sun changes throughout a year . • Kepler found that orbits might change due to gravitational effects from, or collisions with, other objects in the solar system. • He also found that the planets move faster when they are closer to the Sun and slower when they are farther away from the Sun. Kepler’s third law States that the square of the ratio of the periods of any two planets revolving around the Sun is equal to the cube of the ratio of their average distances from the Sun. Thus, if the periods of the planets are TA and TB, and their average distances from the Sun are rA and rB, Kepler’s third law can be expressed as follows: 2 TA rA = TB rB NOTE Kepler’s first and second law applies to each planet , moon and satellite individually. Kepler’s third law relates motion of two objects around a single body. 3 Challenge • It is said that Isaac Newton watched an apple fall and this led to his theory of gravity. • He suggested that there was a force acting on the apple to make it fall. • He extended that idea to all objects, including our planet, the Moon and the Sun. He called it the gravitational force. Factors that affect gravity The effect of mass on gravity The effect of distance on gravity 1. Mass 2. Distance Follows inverse square law CHECKPOINT Law of Universal Gravitation 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 Relation between Kepler’s Third Law and Universal Law of Gravitation Write the final answer in days. To calculate the orbital speed of a satellite To calculate the orbital period of a satellite Vocabulary - satellite A satellite is an object in space that orbits or circles around a bigger object. There are two kinds of satellites: natural (such as the moon orbiting the Earth) or artificial (such as the International Space Station orbiting the Earth). GUIDED PRACTICE What is pressure? 𝑚 = 5.97 × 10 𝑘𝑔 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 𝑟 = 6 ⋅ 38 × 10 𝑚 Pressure is the amount of force (F), in newtons applied perpendicular to the surface of an object per unit area (A) in m2. 𝑚 = 5.97 × 10 𝑘𝑔 𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐 𝑟 = 6 ⋅ 38 × 10 𝑚 SI Unit of Pressure The SI unit of pressure is the pascal (Pa). 1 pascal is the pressure exerted by a body that applies a force of 1 N over an area of 1 m2.