Gravitation

This chapter explains gravitation, the force of attraction between any two objects in the universe. You will study Newton's universal law of gravitation: the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, F = G m1 m2 / d^2, where the universal gravitation constant G is 6.673 x 10^-11 N m^2/kg^2. This force keeps the Moon in orbit around the Earth, holds the planets around the Sun and causes tides. You will learn about free fall and the acceleration due to gravity g, about 9.8 m/s^2, which does not depend on the mass of the falling object, and apply the equations of motion with g. You will distinguish mass, the quantity of matter, from weight, the force with which the Earth attracts an object, W = mg, and see why weight on the Moon is one-sixth of that on Earth. Finally, you will study thrust and pressure, buoyancy, why objects float or sink, and Archimedes' principle.

Detailed Worksheet: Gravitation Section A - Definitions (10 marks) 1. State the universal law of gravitation and write its mathematical form. (2 marks) 2. What is free fall? What is meant by acceleration due to gravity? (2 marks) 3. Distinguish between mass and weight on three points. (2 marks) 4. Define thrust and pressure. Write the SI unit of pressure. (2 marks) 5. What is buoyancy? State Archimedes' principle. (2 marks) Section B - Calculations and Applications (15 marks) 6. The mass of the Earth is 6 x 10^24 kg and that of the Moon is 7.4 x 10^22 kg. If the distance between them is 3.84 x 10^5 km, find the gravitational force exerted by the Earth on the Moon. (G = 6.67 x 10^-11 N m^2/kg^2.) (3 marks) 7. A ball is thrown vertically upwards with a velocity of 49 m/s. Find the maximum height it reaches and the total time it takes to return to the thrower's hand. (Take g = 9.8 m/s^2.) (3 marks) 8. A stone is released from the top of a tower of height 19.6 m. Find its final velocity just before touching the ground and the time taken. (Take g = 9.8 m/s^2.) (3 marks) 9. An object has a mass of 10 kg. What is its weight on the Earth? What will be its mass and weight on the Moon? (Take g = 9.8 m/s^2 on Earth.) (3 marks) 10. A wooden block of mass 5 kg has dimensions 40 cm x 20 cm x 10 cm. Find the pressure it exerts on a table top when it lies on the face of 20 cm x 10 cm and when it lies on the face of 40 cm x 20 cm. (Take g = 9.8 m/s^2.) (3 marks) Section C - Diagrams (10 marks) 11. Draw a diagram showing the motion of a stone tied to a thread and whirled in a circle, and explain how it helps us understand the motion of the Moon around the Earth. (4 marks) 12. Draw a labelled diagram of the activity in which an empty plastic bottle is pushed into a bucket of water, showing the upward force. Explain the observation. (3 marks) 13. Draw a labelled diagram of a stone suspended from a spring balance being lowered into water, showing the change in reading. Relate it to Archimedes' principle. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Show that the value of g on the Earth's surface is given by g = GM/R^2. Calculate g using M = 6 x 10^24 kg and R = 6.4 x 10^6 m. Why is g less at the poles than at the equator? Correct the statement if it is wrong. (5 marks) 15. Explain why (i) a sharp knife cuts better than a blunt one (ii) school bags have wide straps (iii) a camel can walk easily on sand (iv) a ship made of iron floats while an iron nail sinks (v) a person feels lighter while swimming. (5 marks) 16. If the distance between two objects is halved and the mass of one object is doubled, how does the gravitational force between them change? Why does a feather fall more slowly than a coin in air but at the same rate in a vacuum? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Write the formula, convert to SI units and give the unit with every answer.