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A-Level Falling freely, the gravitational potential energy of a uniform field, and how air resistance changes the motion
What the A-Level syllabus expects for Falling freely, the gravitational potential energy of a uniform field, and how air resistance changes the motion, and how to practise it.
What the syllabus expects
- Explain and apply weight, the force a mass undergoes once placed in a gravitational field
- Set out how an object moves when it travels at steady velocity along one axis while accelerating uniformly along the perpendicular axis
- Starting from the definition of work, obtain ∆Ep = mg∆h for shifts in gravitational potential energy across a uniform field
Scope: for example the field close to Earth's surface - Bring ∆Ep = mg∆h to problems from memory
- Give a non-numerical account, in terms of forces and energy, of how objects descend through a uniform gravitational field against drag, eventually reaching terminal velocity
How it's examined
Questions on this topic most often ask you to explain, state. About 3% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (3 marks)
An aircraft travels in a horizontal line at a constant speed of 84 m s⁻¹, cruising 120 m above the ground. As the aircraft passes directly over a fixed point O, a package B is dropped. A while later, package B lands on a truck T of height 2.0 m that is driving along a flat road at a steady speed v. At the moment B is dropped, truck T is x₀ = 140 m away from point O. (a) Work out how long package B is in the air before it hits truck T.
Show the worked answer
The package is dropped from 120 m and lands on the top of a 2.0 m high truck, so it falls a vertical distance: h = 120 − 2.0 = 118 m. The initial vertical velocity is zero, so h = (1/2) g t². t = sqrt(2h/g) = sqrt(2 x 118 / 9.81) = sqrt(24.06) = 4.9 s. (The horizontal aircraft speed of 84 m s⁻¹ does not affect the time of fall.)
Example 2 (2 marks)
(c) If air resistance can no longer be ignored, state and explain what happens to the maximum height reached.
Show the worked answer
The maximum height reached is reduced (lower). On the way up, air resistance acts downward because it always opposes the direction of motion, so it adds to the weight. The total retarding force is therefore greater than weight alone, the body decelerates more rapidly and loses kinetic energy faster, coming momentarily to rest after a shorter upward distance, i.e. at a lower maximum height.
More A-Level H2 Physics topics
Physical quantities, units, measurement uncertainty and vector basics · Types of force, turning effects and conditions for equilibrium · Kinematics, uniformly accelerated motion, momentum and Newton's laws · Energy stores and transfers, work, kinetic and potential energy, fields, power and efficiency · Impulse and the conservation of momentum and energy · Kinematics of uniform circular motion and centripetal acceleration · all of A-Level H2 Physics