Interactive module First-year engineering dynamics
Force, Mass and Acceleration
What tension does an elevator cable carry? How steep can a ramp be before a crate slides, how fast can a car take a curve, and how hard does the seat push on you at the top of a loop? Newton's second law, \(\sum\Fvec = m\avec\), answers all of these, once the forces are drawn correctly. Eight short lessons, with animated figures and questions that check your work, take you from free-body diagrams to banked curves and systems of particles.
- 8 lessons
- 280 min of lessons
- Works offline
Learning outcomes
By the end of the module you can:
- State Newton's laws of motion and use \(\sum\Fvec = m\avec\) with mass, weight and SI units, in an inertial frame. (Lesson 1)
- Draw free-body and kinetic diagrams for a particle, and follow a procedure from the diagrams to the equations of motion and the motion. (Lesson 2)
- Write the equations of motion in rectangular components, with static and kinetic friction, on inclines and with forces at an angle. (Lesson 3)
- Analyze particles joined by cords over pulleys, including dependent motion through a movable pulley. (Lesson 4)
- Integrate the equation of motion when the force depends on time, position or velocity, and find terminal velocities. (Lesson 5)
- Apply \(\sum F_t = m\,dv/dt\) and \(\sum F_n = mv^2/\rho\) to flat and banked curves, conical pendulums, crests, dips and loops. (Lessons 6–7)
- Apply \(\sum\Fvec = m\avec_G\) to systems of particles, find internal forces by isolating parts, and choose between force, energy and momentum methods. (Lesson 8)
How to use this module
Before you start: you should be comfortable with the kinematics of a particle in straight lines and on curved paths, including normal and tangential components (the Curvilinear Motion module), vector components, and integrals of simple polynomials. The module uses the notation of Hibbeler's Engineering Mechanics: Dynamics (\(\sum\Fvec = m\avec\), \(\mu_s\), \(\mu_k\), \(a_n = v^2/\rho\)); Beer & Johnston and Meriam & Kraige use the same ideas with small differences in notation, pointed out where they occur.
Work through the lessons in order. The times allow for working the examples on paper and doing the checks. A suggested plan in four sittings:
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Lessons 1–390 min
Newton's second law, free-body and kinetic diagrams, and rectangular coordinates with friction and inclines.
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Lessons 4–575 min
Connected particles and pulleys, then forces that vary with time, position or velocity.
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Lessons 6–8115 min
Normal and tangential coordinates, banked curves, crests and loops, and systems of particles.
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Practice Lab and Self-Check Quiz65 min
About 30 min of practice on the topics you found hardest, then the 35-minute quiz.
About 6 h in total:280 min of lessons, 30 min of practice, 35 min for the quiz
Get the most out of it
- Keep pencil and paper handy
Try each worked example yourself before you open its solution, and draw every free-body diagram.
- Do the checks
Every lesson has “Check your understanding” questions with hints and full solutions. You can type answers like
12*9.81*sin(25)or(4-1.6)*9.81/12. - Practice until it is routine
The Practice Lab generates unlimited problems, each with a worked solution.
- Test yourself at the end
The Self-Check Quiz gives a score, solutions and a results page you can print or save as a PDF.
- Track your progress
Tick “Mark this lesson complete” at the end of each lesson. A ✓ appears here and in Contents; it is saved in this browser only.
- Keep the formulas close
Print the Formula Sheet, and look up terms in the Glossary.
Lessons
Each lesson has interactive figures, worked examples and questions with instant feedback.
Practice, tools and reference
Use these alongside the lessons, or on their own when you revise.
Requirements
Any modern browser. Works offline.
- A current version of Chrome, Edge, Firefox or Safari, with JavaScript on. A laptop or desktop screen works best; the pages also fit tablets and phones.
- No internet connection, installation or account. Everything is inside this folder.
- Your progress is saved in this browser on this device. Private or incognito windows do not keep it.
Something not working? Read README.txt in the module folder for how to open the module and fix common problems.