Topic Physics 2 a Acceleration due to gravity

Topic – Physics 2 a Acceleration due to gravity Key words – Positive, negative, acceleration, velocity, time, gravity

Topic – Physics 2 a Falling bodes or acceleration due to gravity • Consider the situation when a ball is thrown into the air and then returns to the same height from which it is thrown. Fill in the values below to show your understanding of velocity and acceleration at different points of the journey • On Earth the acceleration due to gravity is approximately 9. 8 ms-2. An object gains or looses 9. 8 ms-1 every second.

Topic – Physics 2 a • In reality, when an object falls, terminal velocity is quickly reached and a constant velocity for the fall obtained as the downwards acceleration equals the upwards force of air resistance. • Gravity • air resistance

Topic – Physics 2 a Uniform acceleration • As acceleration due to gravity is a uniform acceleration, we can use Newton’s equations of motion in solving problem. Instead of ‘a’, we use ‘g’ to represent acceleration due to gravity. In addition, direction now becomes important (for up and down problems) and must be specified. • down for positive • up negative.

Topic – Physics 2 a Formulas now become • g=(v-u) t • v = u + gt • s = ut + ½ gt 2 • v 2 = u 2 + 2 gs where: g = acceleration due to gravity (ms-2) s = displacement (s) u = initial velocity (ms-1) v = final velocity (ms-1) t = time (s)

Topic – Physics 2 a Example 1 • Two children are dropping stones from a bridge to the water below to try and hit the leaves floating by. If one child holds a stone 15. 0 m above the water, calculate • how long before the stone hits the water. • the final velocity of the stone just as it hits the water. • u = 0 ms-1 • s = 15 m • g = 9. 8 ms-2 s = ut + ½ gt 2 v = u + gt

Topic – Physics 2 a Example 1 - answers • Two children are dropping stones from a bridge to the water below to try and hit the leaves floating by. If one child holds a stone 15. 0 m above the water, calculate • how long before the stone hits the water. • the final velocity of the stone just as it hits the water. • • • u = 0 ms-1 s = 15 m g = 9. 8 ms-2 s = ut + ½ gt 2 15 = 0 + (0. 5 x 9. 8 x t 2) 15 = 4. 9 t 2 t= √ 15+4. 9 t = 1. 7496 t = 1. 75 s v = u + gt = 0 + (9. 8 x 1. 7496) v = 17. 1 ms-1

Topic – Physics 2 a Example 2 • A ball is thrown up into the air at 12. 0 ms-1 How long was it in the air if it was caught at the height it was thrown from? • u = -12 ms-1 • v = +12 ms-1 • g = 9. 8 ms-2 • t = v-u g

Topic – Physics 2 a Example 2 - answers • A ball is thrown up into the air at 12. 0 ms-1 How long was it in the air if it was caught at the height it was thrown from? • u = -12 ms-1 • v = +12 ms-1 • g = 9. 8 ms-2 • t = v-u g • t= 12(-12) 9. 8 T= 2. 4 s

Topic – Physics 2 a Example 3 • In a dive, a competitor springs 1. 70 m into the air, turns and dives into the water below. If the diving board is 10. 0 m above the water, and the initial velocity of the diver is 5. 77 ms-1, how long is the diver in the air? with solver then s = ut + ½ gt 2 OR is you don’t have a calculator with solver function v 2 = u 2 + 2 as u = 5. 77 ms-1 s = -10 m g = -9. 8 ms-2 T = v-u g

Topic – Physics 2 a Example 3 - answers • In a dive, a competitor springs 1. 70 m into the air, turns and dives into the water below. If the diving board is 10. 0 m above the water, and the initial velocity of the diver is 5. 77 ms-1, how long is the diver in the air? with solver then s = ut + ½ gt 2 -10 = 5. 77 t + -4. 9 t 2 + 5. 77 t + 10 = 0 t = 2. 13 s OR is you don’t have a calculator with solver function v 2 = u 2 + 2 as = (5. 77)2 + (2 x -9. 8 x -10) = 33. 2929 + 196 u = 5. 77 ms-1 = √ 229. 2929 s = -10 m v = 15. 14 ms-1 down g = -9. 8 ms-2 T = v-u = -15. 14 -5. 77 g -9. 8 T= 20. 91 = 2. 13 s 9. 8