Resultant work changes kinetic energy
The total work done by the forces acting on an object equals its change in kinetic energy. Braking is a useful example: resistive forces reduce the kinetic energy.
Follow the reasoning
- Calculate initial and final kinetic energies.
- Include the work of every force that acts along the displacement.
- Relate the net work to the energy change.
Try it in a past paper 1
Open the question, then use its mark scheme to check your work.
Question 1
Use a car’s velocity–time graph to find braking force, distance and work.
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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 (4)
- 3.3.1(a) Define work done by a force and the unit joule.
- 3.3.1(b) Use W = F x cos θ for work done by a force.
- 3.3.1(c) State and apply the principle of conservation of energy.
- 3.3.2(a) Define and calculate kinetic energy, Ek = ½mv², and derive it from first principles.