Acceleration due to Gravity (OCR A Level Maths: Mechanics)

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

(in which case distance is the magnitude of displacement)

• • … 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 or 3 significant figures
  • You may lose marks if you leave your answer as more than 3 significant figures

(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.