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Free fall motion 1 Three objects are let go from the same level. A The 1-kg object falls fastest. B The 3-kg object falls fastest. C The combined 1 kg object falls fastest. D None of the 1 kg 3 kg 3 kg above. 2 Car A is moving to the left and decelerating... … car B is moving to the right and accelerating. A decelerating B accelerating A decelerating B accelerating Take left as positive direction, give the sign of the following quantities: Car A Car B Velocity + Acceleration 1 Falling objects In air, a coin falls faster than a piece of paper. In a vacuum, they fall at the same rate. The difference, in air, is due to air resistance... having a greater effect on light bodies than on heavier bodies. 2 Reading graphs 0.8 s-t graph of free fall motion Position (m) 0.6 0.4 0.2 0.20 0.30 0.4 0.50 0.60 0.70 time (s) v-t graph of free fall motion 3.5 velocity (m/s) Linear Fit 3.0 m ( Slope ) b ( Y Intercept ) 9.4174 3.0252 r 0.9975 Standard Deviation m 0.1836 Standard Deviation b 0.0945 2.0 slope <9.8 m s–2 1.0 Due to air resistance. 0.20 0.30 0.4 0.50 0.60 0.70 time (s) Q1 In our daily life, the lighter... In our daily life, the lighter objects usually fall slower because A it is a physical law. B it is an illusion. C there is air resistance. D there is measuring error. Q2 True or false... The acceleration of a free falling object increases as it falls faster and faster. (T/F) Q3 True or false... The acceleration due to gravity is larger for heavier objects on Moon. (T/F) Q4 Draw the s-t, v-t and... Draw the s-t, v-t and a-t graphs of a freely falling object from rest. (downwards: +ve.) s t Q4 Draw the s-t, v-t and... Draw the s-t, v-t and a-t graphs of a freely falling object from rest. (downwards: +ve.) s v slope t point t Q4 Draw the s-t, v-t and... Draw the s-t, v-t and a-t graphs of a freely falling object from rest. (downwards: +ve.) v a slope point t t 2 Acceleration due to gravity If resistance is negligible... … a body falls freely under gravity with uniform acceleration. acceleration due to gravity g Accepted value = 9.8 m s–2 Take g 10 m s–2 for simplicity 2 Acceleration due to gravity momentarily at rest a = –10 m s–2 rises up, speed a = –10 m s–2 The ball is thrown vertically upwards u = 40 m s–1 a = –10 m s–2 2 Acceleration due to gravity When the ball falls, its speed at the rate of 10 m s–2 Video Simulation 3 Solving free fall problems The equations of motion... for uniformly accelerated motions... … apply to falling objects. g 10 m s-2 Example 10 (a) How long does the stone Central Plaza take to reach the ground? 374 m Example 10 u=0 s = 374 m a = g = 10 m s–2 t=? (a) Applying s = ut + 1 at 2 2 1 374 = 0 t + 10 t 2 2 t = 8.65 s Example 10 (b) With what speed does Central Plaza the stone hit the ground? 374 m Example 10 u=0 s = 374 m a = g = 10 m s–2 v=? (b) Applying v 2 u 2 = 2as v 2 0 = 2 10 374 v = 86.5 m s1 Example 10 u=0 s = 374 m a = g = 10 m s–2 v=? The stone hits the What happens if the stone hits ground with a your head? speed of 86.5 m s-1 (or 311 km h-1)! Example 11 Peter throws a stone vertically upwards from the ground with a speed of 20 m s–1. (a) How high does the stone rise? Example 11 (a) How high does the stone rise? Upward journey: u = 2 m s–1 momentarily at rest v=0 (at highest point) a = 10 m s–2 (downwards ve) s=? decelerates as it rises up Example 11 (a) How high does the stone rise? Applying v 2 – u 2 = 2as v 2 u2 02 (2) 2 s= = 2a 2 (10) = 0.2 m (upwards) Example 11 (b) How long does it take to rise up & to return to the ground? Applying s = ut + 1 at 2 2 1 0 = 5 t + (–10) t 2 2 t = 0 or t = 0.4 s The stone is at s = 0 twice initially at 0 s and on its return to the ground after 0.4 s. Example 11 (c) With what speed does the stone hit the ground? Applying v = u + gt = 2 + (–10) 0.4 = –2 m s1 The stone hits the ground on its return with a speed of 2 m s-1. Example 11 (d) Sketch the (i) s-t graph (ii) v-t graph (iii) a-t graph of the stone’s motion. Example 11 s-t graph displacement/m 0.2 time/s 0.2 0.4 Example 11 v-t graph velocity/m s-1 2 time/s –2 0.2 0.4 Example 11 a-t graph acceleration/m s-2 time/s –10 (For questions 1 to 5.) A ball is fired upwards with u = 5 m s1 from the top of a building... Q1 When the ball goes up... When the ball goes up, the speed it loses in 10 m s–1 each second is __________. A ball is fired upwards with u = 5 m s–1 from the top of a building. It hits the ground 2 s later. (Take g = 10 m s–2. Neglect air resistance.) Q2 When the ball falls down... When the ball falls down, the speed it gains in 10 m s–1 each second is _________. A ball is fired upwards with u = 5 m s–1 from the top of a building. It hits the ground 2 s later. (Take g = 10 m s–2. Neglect air resistance.) Q3 True or false... True or false: Its velocity changes direction as it passes the highest point. (T/F) A ball is fired upwards with u = 5 m s–1 from the top of a building. It hits the ground 2 s later. (Take g = 10 m s–2. Neglect air resistance.) Q4 True or false… True or false: Its acceleration is zero at the highest point. (T/F) A ball is fired upwards with u = 5 m s–1 from the top of a building. It hits the ground 2 s later. (Take g = 10 m s–2. Neglect air resistance.) Q5 What is the velocity... What is the velocity of the ball when it hits the ground? (Take upward direction as +ve) A s = 0 as it hits the ground. v2 = u2 + 2as = 52 + 0 = 25 v = 5 m s-1 downwards Q5 What is the velocity... What is the velocity of the ball when it hits the ground? (Take upward direction as +ve) B v = u + gt = 5 + 10 2 = 25 m s1 The velocity is 25 m s1 downwards. Q5 What is the velocity... What is the velocity of the ball when it hits the ground? (Take upward direction as +ve) C First, consider the rise. It momentarily stops at the highest point: t = (0 u)/a = (0 5)/(10) = 0.5 s Then, consider the fall. v = 0 + at = 0 + a (2 t) = 0 + (10) (2 0.5) = 15 m s1 The velocity is 15 m s1. Q5 What is the velocity... What is the velocity of the ball when it hits the ground (Take upward direction as +ve) A s = 0 as it hits the ground... B v = u + gt... C First, consider the rise. It momentarily stops...

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