AQA A Level Maths: Mechanics复习笔记2.3.3 Acceleration due to Gravity

What is acceleration due to gravity?

• If motion is vertical and no other forces are acting on a particle, the acceleration of the particle will be due to gravity
  • Acceleration due to gravity is denoted by the letter g
  • The value for gravity on Earth varies depending on location (the average value is 9.80665)
  • Take g = 9.8 m s-2 unless told otherwise
  • It is often easier to leave working in terms of g as it sometimes cancels out or it can be calculated at the end
  • Some questions may ask for the answer to be left in terms of g
• Gravity will always act in the downwards direction towards the earth
  • If you decide upwards is the positive direction, then a = -g
  • If you decide downwards is the positive direction then a = g
  • It is important to be clear about which direction you have decided is positive

Displacement or Distance?

•  There is a difference between displacement and distance
• It is more pronounced in vertical motion problems
  • Particles typically travel in both directions (up and down)
  • What goes up must come down!
• Displacement, s, is a vector
  • It is the position of a particle (at time t) relative to its starting position
  • It only takes into account where the particle started and ended
  • If a particle has returned to its starting position then its displacement will be zero
• Distance could be …
  • … the distance from the start

• • … the distance travelled
  • … the distance from the origin

(the origin is not necessarily the starting position)

• • … the distance from another particle

• Read the question carefully to be clear about which of these you are finding

How do I solve suvat problems involving gravity?

•  Virtually the same as suvat in 1D for horizontal motion
  • Follow the same steps and be careful with negatives
• You might have to spot that gravity is the acceleration by seeing the phrases:
  • "falling freely"
  • "projected"
  • "thrown/dropped"
• A diagram is important to help make clear …
  • … the positive direction of motion
  • … the way in which acceleration relates to the positive direction
  • … differences between displacement and distance
• Particles moving upwards will reach a maximum height
  • At the maximum height, velocity is instantaneously zero, v = 0
• If you use the value 9.8 for g then your final answer must be written as a decimal to 2 significant figures
  • In general the accuracy of your final answer should match the accuracy of the value used for g (1sf for g=10, 2sf for g=9.8 and 3sf for g=9.81)

(a)  Find the maximum height the toy rocket reaches.

(b)  Find the time taken from the instant the toy rocket is projected to the instant it returns to the ground.