Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Theoretical astronomy wikipedia , lookup
Lunar theory wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Astronomical unit wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Gravitational wave wikipedia , lookup
IB Physics Topic 6 Fields and Forces Period ______________________ Name ________________________________ 1 This is a blank page 2 6.1 Gravitational Force and Field (2 hr) Activity 611 Measuring Gravitational Force between two objects (NB) Activity 612 Investigating Gravitational Field around a mass (NB) Activity 613 Investigating the local gravitational acceleration (NB) Read Tsokos pp 127-130 Read Cutnell pp 96-103(force) G-acc pp 44, 47, 147-151 (artificial G) Assignment A611 Tsokos pp130,131#1 to 8 3 6.1 Gravitational Force and Field The Newton’s universal law of gravitation “Newton proposed that the attractive force of gravitation between two point masses is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the two masses. ” (Newton’s Principia) Important details: Equation: Where m1, m2 are masses of the particles, r is the separation between them, and G is the Newton’s constant of universal gravitation, G = _____________________________ Summary 4 <Sample Questions> Q1 Find the attractive force between the sun and the earth. (mearth = 5.98x1024 kg. msun = 1.99x1030 kg. the average distance between earth and sun is 1.5x1011 m) _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Q2 If the distance is doubled, what happen to the gravitational force between them? How happens if the distance is tripled or halved? _________________________________________ _________________________________________ _________________________________________ _________________________________________ Summary 5 Weight and Gravitational Force <Sample questions> Q3 Find the acceleration due to gravity (or gravitational field strength) on a planet 10 times as massive as the earth and the radius 20 times as large. _________________________________________ _________________________________________ _________________________________________ Q4 Find the acceleration due to gravity at a height of 300 km from the surface of earth. (The average radius of the earth is rE = 6.378x106 m) _________________________________________ _________________________________________ _________________________________________ Summary 6 The Gravitational Field Strength The magnitude of a gravitational field is known as Gravitational Field Strength. This is defined as the gravitational force that acts on per unit mass, or on each kilogram, of a body in the field. (The gravitational field strength at a certain point is the force per unit mass experienced by a small point mass m at that point.) The force experienced by a small point mass m placed at distance r from a mass M is So the gravitational field strength (F/m) of the mass M is The unit of gravitational field strength is Nkg–1 or ms2 Gravitational Field Diagrams: (1) Gravitational Field around a point mass is radial (2) Gravitational field above a flat surface Summary 7 Graphing the Gravitational Field caused by a non-point mass What do you see in this graph? _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre. Summary 8 The inverse square law Gravitational Field vs. position Equation of the curve Summary 9 Q5 Two stars have the same density but star A has double the radius of star B. Determine the ratio of the gravitational field at the surface of each star. _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Q6 Show that the gravitational strength at the surface of a planet of density has a magnitude given by 𝑔 = 4𝑔𝜋𝜌𝑅 3 _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Summary 10 Determine the Gravitational Field that is due to one or more point masses 1. A 50 kg piece of space junk is falling towards Earth from a height of 1 000 km above the Earth’s surface (mass of Earth is 5.98x1024 kg, radius is 6.38x106 m). Ignoring air resistance, determine: a. The gravitational field strength at this high ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ b. The direction of the gravitational field at this location ____________________________________________________ ____________________________________________________ c. The acceleration of the space junk at this height as it falls ____________________________________________________ ____________________________________________________ d. The value of the ratio 𝑓𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑎𝑡 500 𝑘𝑚 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 𝑓𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑎𝑡 500 𝑘𝑚 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 11 2. A 10.0 kg watermelon falls a short distance to the ground. If the Earth has a radius of 6.38x106 m (6 380 km)and a mass of 5.98x1024 kg, calculate: a. The gravitational force that the Erath exerts on the watermelon. ____________________________________________________ ____________________________________________________ ____________________________________________________ b. The gravitational force that the watermelon exerts on the Earth. ____________________________________________________ ____________________________________________________ ____________________________________________________ c. The acceleration of the watermelon toward the Earth ____________________________________________________ ____________________________________________________ ____________________________________________________ d. The acceleration of the Earth toward the Watermelon ____________________________________________________ ____________________________________________________ ____________________________________________________ 12 3. Three identical 8-kg point masses m1, m2 and m3 are placed on x = -2, 0, and +8 respectively on a linear coordinate system that is located somewhere in space far away from all other space objects. a. Draw a free-body diagram (force diagram) and determine the net gravitational force exerting on m1. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ b. Draw a free-body diagram (force diagram) and determine the net gravitational force exerting on m2. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ Summary 13 4. Three identical 5-kg point masses m1, m2 and m3 are placed on (0,0), (0,3) (4,3) respectively on a plane coordinate system that is located somewhere in space far away from all other space objects. a. Draw a free-body diagram (force diagram) and determine the net gravitational force exerting on m1. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ b. Draw a free-body diagram (force diagram) and determine the net gravitational force exerting on m2. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ Summary 14 Activity 611 Measuring Gravitational Force between two objects (Lab NB) Newton proposed that the attractive force of gravitation between two point masses is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the two masses. Essential Question: How do you determine the gravitational force or gravitational attraction between two objects at your choice? 1. Identify the chosen ones. 2. Decide the procedure and divide the work among partners 3. Carry it out collaboratively 4. Check your findings and analyze it. 15 Activity 612 Investigating Gravitational Field around a Mass (Lab NB) The Gravitational Field vs. Position graph shows the progression of the gravitational field along a line between the center of the field creator and the center of the object in the field. Data Table Distance RE), R in between m and M (in RE 2 RE 3 RE 4 RE 5 RE 16 Gravitational Field Strength, g, Nkg-1 or ms-2 9.8 2.5 1.1 0.6 0.4 (1) Design a data table to show the Linearization of the Curve (2) Plot the graph with the data (include the title, the axes, the units, and a brief description of the graph) (3) Write the equation for the line (4) What information may be found with the Extrapolate and Interpolate methods? Describe the significance. 17 Activity 613 Investigating the local gravitational acceleration (Lab NB) The gravitational field is expressed with the gravitational acceleration which includes magnitude and direction. Essential Question: How do you determine the gravitational field near the surface of earth? 5. Identify the location. 6. Decide the procedure and divide the work among partners 7. Carry it out collaboratively 8. Check your findings and analyze it. 18 Extended Questions: (1) How to create an artificial gravitational field? (2) How to create a zero-gravity (microgravity) environment? (3) How does Einstein’s model differ from Newton’s model? 19