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Physics · 10 / 12

Forces and energy: choose the system

Final-year concepts · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Units: numbers have dimensionsEquations: keep the balance level
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

A force represents an interaction. In an inertial frame at constant mass, the vector sum of forces is mass times acceleration. Kinetic energy is mv²/2 and does not depend on velocity’s direction. An energy balance identifies transfers and changes rather than assuming every energy is constant.

F=m*a
THE PICTURE TO REMEMBERForces and energy: choose the system
  1. 01System
  2. 02Interactions
  3. 03Net force
  4. 04Acceleration or energy balance

WORKED EXAMPLE

From principle to reasoning

A 2 kg mass under a net 6 N force accelerates at 3 m/s². At 4 m/s its kinetic energy is 16 J.

Solve a problem in this subject

  1. Draw the system

    Define the studied object, reference frame and positive axis. A force diagram shows external interactions acting on the system.

  2. Sort quantities

    Separate data and unknowns; convert units before substitution. 36 km/h = 10 m/s, so never insert 36 into a formula expecting SI speed.

  3. Write the model

    Choose a law matching assumptions: constant acceleration, thin lens, ohmic resistor. Isolate the unknown symbolically before rounding.

  4. Interpret

    Check dimensions and signs. Negative velocity gives direction on the chosen axis. Discuss scale and model limitations.

YOUR TURN

01 · Try before checking

At fixed mass, what happens to kinetic energy when speed doubles?

One hint

Speed is squared.

Reveal and understand the solution

(2v)² = 4v², so kinetic energy is multiplied by four.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

A 2 kg body has net force 6 N. Find acceleration.

A hint to get started

Use the net force, not an isolated force.

Step-by-step solution
  1. ΣF = ma.
  2. a = 6/2 = 3 m/s².
  3. Acceleration follows the net force in an inertial frame.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

A 2 kg body moves at 3 m/s. Find kinetic energy.

A hint to get started

Square the speed.

Step-by-step solution
  1. Ec = mv²/2.
  2. Ec = 2 × 9/2 = 9 J.
  3. Doubling speed would quadruple this energy.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

Without friction, an object loses 20 J of potential energy. What happens to kinetic energy?

A hint to get started

Mechanical energy is conserved in this model.

Step-by-step solution
  1. ΔEc + ΔEp = 0.
  2. ΔEp = −20 J, so ΔEc = +20 J.
  3. With friction, dissipative work must be included.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

Use net force and account for directions.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

Choosing a state saves it in this browser. This is your assessment, not a grade.

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