Gravitation. Gravitation

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1 1 Gravitation Newton s observations A constant center seeking force is required to keep an object moving along a circular path. You know that the moon orbits the earth and hence there should be a force pulling the moon towards the center of the path taken by the moon. Where does that force come from? Fruits when ripe fall to the ground. If you throw a ball up in the air, after moving up for a while, it gets pulled back towards the ground. Obviously the ground exerts some force on the fruits and ball. Where does this force come from? In 1660 s, Sir Isaac Newton proposed that the same force that causes the moon to go around the earth pulls the apple towards the ground. Unlike the apple that moves along a straight path towards the ground, the moon moves along a circular path and does not fall to the ground. So how can Newton be correct in his hypothesis? Activity: Roll a ball off the table Place a ball on top of a table. Gently push the ball over the edge and note the horizontal distance travelled by ball - m Repeat the experiment by pushing the ball a little harder. Again measure the horizontal distance travelled by the ball - m. In which scenario does the ball travel more distance in the horizontal direction?

2 2 The earth is not flat but round. What would happen if you continue to increase the force with which you push the ball off the table? Is it possible that the ball could follow a path which is parallel to the surface of the earth? What will happen if you push the ball with even greater force? Newton called this force gravity. Any object that has mass exerts a gravitational force on every other object. Factors influencing gravitational force The gravitational force of attraction depends up on the mass (M) of the object. More the mass, more the gravitational force exerted by the object. In other words the gravitational force is directly proportional to the mass (M) of the object exerting the force. What other factors does it depend up on? Activity: Galileo s experiment at the Tower of Pisa Select two objects different size and weight. If you were to drop both of them from the same height which one of the two do you think would hit the ground first? Go to the terrace of your building and while you drop the two objects simultaneously from the terrace ask you friend to stand on the ground and see which object reaches the ground first. Repeat the experiment with two objects of roughly the same size but different weight. What do you observe? Mass of object (m) Time taken (t)

3 3 What can you infer from your observations? Does the acceleration of the object depend on the mass of the object? (Hint: The initial velocity of the objects is 0 and they all travel the same distance. You can find the acceleration of the objects using the 2 nd equation of motion. You will also find that acceleration is inversely proportional to time 2.) You might want to repeat the experiment a couple of times and note the time. Most likely you will find that the time taken by the same object changes each time. Is this because acceleration due to gravity is changing or because of human error while noting down the time? You might have also observed that if you throw a very light object or an object it takes a lot of time to reach the ground. The time decreases as you increase the mass of the object and then more or less remains the same as you keep increasing the mass. How can you explain this? Is gravity being partial to objects with very less mass? ( ) ( ) ( ) If a = constant then can we say that the gravitation force directly proportional to the mass (m) of the object that is being pulled? The mass of the sun is approximately 332,950 times the mass of the earth. But still the moon orbits the earth and is not pulled away by the sun. Could the gravitational force depend on something besides the mass of the object that is exerting the force?

4 4 Activity: Calculating the effect of distance on gravitational force Radius of earth = r km m Radius of moon s orbit Average speed of moon 60r m 1000 m/s Acceleration due to gravity on the surface of earth 10 m/s 2 Acceleration of moon due to earth s gravity = Calculate ( ) Compare A and B. Definition Universal law of gravitation: Mathematical representation of the Universal law of gravitation:

5 5 You studied that the earth exerts a force on objects. Do the objects on earth all exert a force on the earth? How does the magnitude of the force exerted by the object compare to the force exerted by the earth? If both the forces have the same magnitude then why do we only see objects falling towards the ground and not see the earth moving towards the object? For example, why does the earth not move towards the apple? Sample Problem Calculate the gravitational force of attraction between the earth and yourself. Radius of earth = m. Mass of earth = 6 * kg.

6 6 Acceleration due to gravity Formula to calculate the acceleration due to gravity:

7 7 Sample Problem Calculate the acceleration due to gravity on the surface of Jupiter. Radius of Jupiter ~ 11 times the radius of Earth. Mass of Jupiter ~ 319 times the mass of Earth. Mass and weight Is weight the same as mass? When you weigh something, what are you measuring? Definition Weight: Checkpoint

8 8 Would you weigh more at the poles or at the equator? Why? Would you weigh the same if you were in a spaceship orbiting earth at km? Why? If you were to travel towards the center of the earth would your weight increase or decrease or remain the same? Why? Sample Problem Calculate your weigh on Jupiter?

9 9 Free fall Definition Free fall: Objects in free fall have a uniform acceleration because of gravity (g). Can you rewrite the equations of motion for objects in free fall? Equations of motion for a freely falling object: Note: Since acceleration due to gravity always acts in the downward direction, g is always 9.8 m/s 2. Sample Problem A boy drops a coin from the top of a building which is 10 m high. Find the velocity with which the coin strikes the earth?

10 10 Kepler Years before Newton proposed his law of gravitation; Kepler had proposed the laws of planetary motion. Find out more about Kepler and his laws.

11 11 Questions and Problems Universal Law of Gravitation 1. The universal of Newton's law of universal gravitation is a common source of confusion. The term universal means that. a. the amount of gravitational forces is the same for all objects. b. the acceleration caused by gravity is the same for all objects. c. the force of gravity acts between all objects - not just between the Earth and an object, but even between two people. All objects with mass attract. 2. According to Newton's gravitation law, the force of gravitational attraction between a planet and an object located upon the planet's surface depends upon. Choose all that apply. a. the radius of the planet. b. the mass of the object. c. the mass of the planet. d. the volume of the object. 3. Two objects gravitationally attract with a force of 18 N. If the distance between the two object s centers is doubled, then the new force of attraction is N. 4. Two objects gravitationally attract with a force of 18 N. If the mass of one of the objects are doubled and the distance between their centers is doubled, then the new force of attraction is N. 5. Two objects gravitationally attract with a force of 18 N. If the mass of both of the objects are tripled and the distance between the two objects' centers is doubled, then the new force of attraction is N. Acceleration due to gravity 6. Calculate the acceleration due to gravity on the surface of the moon. Radius of moon = 0.27 times the radius of Earth. Mass of moon = times the mass of Earth. Formula:

12 12 Mass and Weight 7. Orbiting astronauts on the space shuttle are do not have weight in space because. a. there is no gravity in space b. there is no air resistance in space c. there are no scales in space d. the food is terrible and they work all the time e. the astronauts do have weight in space. Free Fall 8. A ball is thrown up with a velocity of 5 m/s. How high will it go before it begins to fall? (g = -9.8 m/s 2 ) Given: Find: Formula: 9. A stone is dropped freely in the river from a bridge. The stone takes two seconds to touch the water surface. Calculate the height of the bridge from the water level. (g = -9.8 m/s 2 ) Given: Find: Formula:

13 A ball is dropped from a height of m. How long does it take for the ball to reach the ground? (g = -9.8 m/s) Given: Find: Formula:

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