Force and Motion

This chapter asks about the difference between distance and displacement, how to determine speed, and why we are hurled forward when a vehicle stops suddenly p. 225. The electric train service (ETS) from Kuala Lumpur reaches Padang Besar in 4 hours 15 minutes compared to 12 hours by diesel train, at a speed of about 160 km h⁻¹ p. 225.

11.1 Linear Motion

Linear motion is the motion of an object in a straight path p. 226. Distance is the total path length travelled by an object, while displacement is the distance of the shortest path that connects two locations in a specified direction p. 226. For example, 80 m + 80 m gives a distance of 160 m, but the displacement is 113.14 m in the northwest direction p. 226. The S.I. unit for distance and displacement is the metre (m) p. 226.

Speed is the rate of change of distance, and average speed is the total distance travelled divided by total time; both are measured in metres per second (m s⁻¹) p. 228. A runner who covers 100 m in 10 s has an average speed of 10 m s⁻¹ p. 228. Velocity is the rate of change of displacement, measured in m s⁻¹, and its positive or negative sign shows the direction of motion p. 229. Acceleration is the rate of change of velocity, a = (v − u) / t, and its S.I. unit is metre per second per second (m s⁻²) p. 230. A bicycle that goes from rest to 4 m s⁻¹ in 5 s has an acceleration of 0.8 m s⁻², and when the brakes are applied its velocity decreases, which is deceleration p. 230. Usain Bolt, starting from rest and reaching 10.44 m s⁻¹ at the 100 m finish line in 9.58 s, has an acceleration of 1.09 m s⁻² p. 231.

A photogate measures very fast motion or short time intervals accurately p. 232. A ticker timer vibrates at 50 vibrations per second (50 Hz), and one tick, the interval between two adjacent dots, represents 0.02 seconds p. 232. A strip of 5 ticks that is 10 cm long takes 0.1 s, so its velocity is 100 cm s⁻¹ p. 232. In Activity 11.2 the tape is cut into 5 strips of 10 ticks, and each strip takes 0.2 s p. 233. Constant spacing between dots shows uniform velocity, spacing that increases uniformly shows uniform acceleration, spacing that decreases uniformly shows uniform deceleration, and spacing that is not constant shows non-uniform velocity p. 234.

11.2 Linear Motion Graphs

The two types of linear motion graph are the displacement-time graph and the velocity-time graph p. 235. On a displacement-time graph, a positive uniform gradient means uniform velocity, a zero gradient means the object is at rest, and a negative gradient means it moves in the opposite direction p. 235. On a velocity-time graph, a positive uniform gradient means uniform acceleration, a zero gradient means constant velocity, and a negative gradient means uniform deceleration p. 236. Velocity is the gradient of a displacement-time graph p. 237. Displacement is the area under a velocity-time graph, and acceleration is its gradient p. 238.

11.3 Gravitational Acceleration and Free Fall

All objects are pulled towards the centre of Earth by Earth’s gravitational force, and a falling object experiences gravitational acceleration, with the symbol g p. 239. In Experiment 11.1, a ticker timer and a weight of mass 50 g are used to determine g, and the steps are repeated with heavier weights p. 240. The value of gravitational acceleration, g, on the surface of Earth is 10 m s⁻² p. 241. An object experiences free fall if it falls due to gravitational force only, and freely falling objects have the same gravitational acceleration whatever their mass and shape p. 241. Free fall actually only occurs in a vacuum, where a chicken feather and a tennis ball released from the same height reach the bottom at the same time p. 241.

When a freely falling object is released, its velocity increases uniformly, and the gradient of its velocity-time graph is the gravitational acceleration p. 242. An object thrown vertically upwards slows down, so its velocity-time graph has a negative gradient, and at maximum height its velocity is zero p. 243. In Experiment 11.2, pieces of paper fall in a cylinder tube with and without air, using a vacuum pump p. 244. Galileo Galilei dropped two spheres of different mass from the Leaning Tower of Pisa sometime from 1589 to 1592 and found that they took almost the same time to reach the ground p. 244.

11.4 Mass and Inertia

Mass is the quantity of matter in an object, its S.I. unit is the kilogram (kg), and it is constant if the quantity of matter does not change p. 246. Inertia is the natural tendency of an object to resist any change in its original state, whether at rest or in motion; it is not a physical quantity, so it has no value and no unit p. 246. When a cardboard is pulled quickly from under a coin, the coin’s inertia keeps it at rest and it falls into the glass p. 246. Newton’s First Law of Motion states that an object remains at rest or in motion with constant speed in a straight line if no external force acts on it p. 246. When a train stops suddenly, the inertia of a passenger keeps the body moving forward p. 246.

The larger the mass of an object, the larger its inertia p. 247. An inertial balance, invented by NASA to determine the mass of objects in outer space, is used in Experiment 11.3 with plasticine of 30 g to 70 g on a hacksaw blade p. 248. A loose hammer head can be tightened by banging the handle on a hard surface, and a wet umbrella can be dried by spinning it and stopping it suddenly p. 249. Cars have airbags, headrests and safety belts to reduce the effects of inertia, and long runways are needed because a heavy aeroplane cannot stop within a short distance p. 249.