Knowledge area 7 of the FE Mechanical exam: 10–15 of the 110 questions. The subtopics NCEES lists, how they are tested and worked practice problems with solutions.
110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.
Or start the free Dynamics, Kinematics, and Vibrations drillFrom the NCEES FE Mechanical CBT exam specifications, knowledge area 7.
Dynamics questions cover motion of particles and rigid bodies: constant-acceleration kinematics, projectiles, Newton’s second law, work-energy and impulse-momentum. Choose the method from what is given: forces and acceleration point to Newton’s law, speeds and distances to work-energy, times and velocities to impulse-momentum. Vibration questions ask for natural frequency, period or the response of a spring-mass-damper system.
On exam day the relationships you need are in the Reference Handbook section on Dynamics. The handbook is the only reference allowed, so practice finding each formula in it rather than memorizing a separate sheet.
Work each problem with your calculator and the handbook, then open the solution.
Problem 1 · Impulse-momentum of rigid bodies
A wheel with a mass moment of inertia of 0.80 kg·m² spins at 1,500 rpm. A brake applies a constant 16 N·m torque. The time to bring the wheel to rest is most nearly:
Answer: B: 7.85 s
ω = 1,500(2π/60) = 157.1 rad/s. Angular impulse: Tt = Iω, so t = 0.80(157.1)/16 = 7.85 s.
Impulse-momentum of rigid bodies · Reference Handbook: Dynamics
Problem 2 · Newton's second law for rigid bodies
A 10 kg block hangs from a light rope wound around a drum of 0.25 m radius. The drum turns in frictionless bearings and has a mass moment of inertia of 2.0 kg·m². Take g = 9.81 m/s². When released, the block's acceleration is most nearly:
Answer: A: 2.34 m/s²
Block: mg − T = ma. Drum: Tr = Iα = I(a/r), so T = Ia/r². Combining: a = mg/(m + I/r²) = 98.1/(10 + 32) = 2.34 m/s².
Newton's second law for rigid bodies · Reference Handbook: Dynamics
Problem 3 · Kinematics of particles
A ball is launched from level ground at 20 m/s and 35° above the horizontal. Neglect air resistance and take g = 9.81 m/s². Its horizontal range on the level ground is most nearly:
Answer: D: 38.3 m
R = v₀² sin 2θ/g = (20)² sin 70°/9.81 = 400(0.9397)/9.81 = 38.3 m. Equivalently, flight time = 2(20 sin 35°)/9.81 = 2.339 s and R = 20 cos 35°(2.339) = 38.3 m.
Kinematics of particles · Reference Handbook: Dynamics
Problem 4 · Kinetic friction
A package is released from rest on a ramp inclined at 30° to the horizontal. The coefficient of kinetic friction is 0.20. Take g = 9.81 m/s². Its speed after sliding 5.0 m along the ramp is most nearly:
Answer: B: 5.66 m/s
a = g(sin 30° − 0.20 cos 30°) = 9.81(0.500 − 0.173) = 3.21 m/s². v = √(2as) = √(2·3.21·5.0) = 5.66 m/s.
Kinetic friction · Reference Handbook: Dynamics
More FE Mechanical practice problems from every knowledge area
Sit the full exam under the real clock
110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.
Or start the free Dynamics, Kinematics, and Vibrations drillThe NCEES FE Mechanical specification lists 10–15 questions on Dynamics, Kinematics, and Vibrations, out of 110. Every examinee gets the same number per knowledge area.
Kinematics of particles; Kinetic friction; Newton’s second law for particles; Work-energy of particles; Impulse-momentum of particles; Kinematics of rigid bodies; Kinematics of mechanisms; Newton’s second law for rigid bodies; Work-energy of rigid bodies; Impulse-momentum of rigid bodies; Free and forced vibrations.
In the NCEES FE Reference Handbook, which appears on screen during the exam: the Dynamics section. Practice with your free copy from MyNCEES so you know where each relationship sits.
Original independent practice questions written to the published NCEES exam specifications. Not affiliated with or endorsed by NCEES (National Council of Examiners for Engineering and Surveying).