Free fall through motion and energy
Motion equations and conservation of mechanical energy give the same speed for a freely falling object. One describes the acceleration; the other tracks energy transfer.
Follow the reasoning
- Define the initial and final heights and speeds.
- Use either the vertical motion equation or an energy balance.
- Check that the height change has the correct sign.
Try it in a past paper 5
Open the question, then use its mark scheme to check your work.
Question 11
Relate a falling object’s speed to its change in height.
Question 24(b)–(e)
Analyse falling motion, improve timing and sketch a bounce.
Question 3(a)–(d)
Resolve projectile velocity and connect its motion with energy and momentum.
Question 4
Connect free fall and projectile motion with energy and velocity components.
Show 1 more paper references
Question 1
Use a bouncing ball’s velocity graph to calculate energy, rebound speed and height.
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Put the ideas to work
Questions are matched by their specification tags. Read the prompt to check how it relates to this connection; use “Report tag issue” if a match seems wrong.
A technician calibrates the spring bumper of a small instrument trolley. Figure 1 shows the force F needed to compress the spring by x from its natural length. The graph is a straight line through (0, 0), (0.020 m, 1.2 N), (0.040 m, 2.4 N) and (0.060 m, 3.6 N). The trolley has mass 0.60 kg. It is released from rest against the spring at compression 0.060 m on a horizontal track. A constant resistive force of 0.60 N opposes the motion as soon as the trolley moves. The spring's mass is negligible and its deformation is elastic. The trolley loses contact with the spring at its natural length. There are no other energy losses. (a) Use the gradient of the force-compression graph to determine the spring constant. [2] (b) Use the graph to calculate the work needed to compress the spring from its natural length to 0.060 m. [2] (c) Calculate the acceleration just after release, stating its direction relative to the bumper. [3] (d) Calculate the speed when the trolley loses contact with the spring. Account for the work done against resistance. [3] (e) Explain why a single constant-acceleration equation cannot describe the whole interval while the trolley is in contact with the spring. [2] (f) Calculate the distance travelled after losing contact before the trolley stops. Use a constant-acceleration equation for this part. [3]
Matched by specification tags
Try this question now →Specification outcomes (5)
- 3.1.2(a)(i) Apply equations of motion for constant acceleration in a straight line, including motion in a uniform gravitational field without air resistance.
- 3.1.2(b)(i) Understand acceleration of free fall g.
- 3.3.2(a) Define and calculate kinetic energy, Ek = ½mv², and derive it from first principles.
- 3.3.2(b) Define and calculate gravitational potential energy, Ep = mgh, and derive it from first principles.
- 3.3.2(c) Explain the exchange between gravitational potential energy and kinetic energy.