← MCAT®

4A: Translational Motion, Forces, Work, Energy, and Equilibrium in Living Systems

Arrows, ramps, wrenches and pendulums: the mechanics half of Foundational Concept 4, drawn as motion rather than asserted as formulas.

14 topics · 61 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

4A. Units, Dimensions, and Dimensional Analysis

  1. How it worksHow do you strip an equation down to kilograms, meters and seconds and watch both sides balance?
  2. Worked exampleShow me how to turn 120 mmHg into pascals by cancelling units, with no calculator anywhere.
  3. Worked exampleFind what units the constant in Poiseuille's law must carry for flow to come out in cubic meters per second.
  4. Going furtherWhat breaks about a formula when a quantity with units gets pushed inside a logarithm?
Your turneasy1 of 3
A cuff reads a systolic pressure of 144 mmHg. Taking 1 mmHg = 133 Pa, convert that gauge pressure to pascals.

4A. Vectors, Components, and Vector Addition

  1. How it worksHow does one slanted arrow split into a horizontal piece and a vertical piece that rebuild it?
  2. Worked exampleFind the horizontal and vertical parts of a 50 N tendon force angled 37 degrees above horizontal.
  3. How it worksWalk me through laying two force arrows tip to tail and reading the resultant off the triangle.
  4. Worked exampleFind the resultant of a 30 N pull due east combined with a 40 N pull due north.
  5. Common mistakeWhy isn't the size of a vector sum simply the two sizes added together?
Your turneasy1 of 3
A tendon pulls on a bone with a force of 69 N directed 37 degrees above the horizontal. Using sin 37 = 0.60, find the vertical component of that pull.

4A. Speed, Velocity, and Acceleration

  1. How it worksHow does the steepness of a position-versus-time curve become velocity at every instant?
  2. How it worksHow does the shaded area under a velocity-versus-time curve hand back the displacement?
  3. Worked exampleFind how far a car slides while braking from 20 m/s to a stop at 4 m/s squared.
  4. Common mistakeWhy doesn't a negative acceleration always mean something is slowing down?
Your turneasy1 of 3
A car brakes from 24 m/s to a complete stop with a constant deceleration of 5 m/s2. Find the distance it covers while stopping.

4A. Projectile Motion

  1. How it worksHow does splitting a flying ball into steady sideways motion and falling motion solve the whole path?
  2. How it worksWalk me through why the velocity arrow tips over steadily as a thrown ball arcs to the ground.
  3. Worked exampleFind the horizontal range of a ball launched at 20 m/s, 30 degrees above flat ground.
  4. Worked exampleFind how long a diver is airborne after leaving a 10 m platform moving sideways at 3 m/s.
  5. Common mistakeWhy isn't some forward force still pushing a thrown ball along after it leaves the hand?
Your turnmedium1 of 3
A diver leaves a 33 m platform moving horizontally at 6 m/s. Using g = 10 m/s2, find how far from the base of the platform the diver enters the water.

4A. Newton's Three Laws and Inertia

  1. How it worksHow does a free-body diagram collapse a messy pile of pushes into one net force arrow?
  2. Worked exampleFind the acceleration of a 60 kg skater feeling a net forward force of 150 N.
  3. How it worksHow can action and reaction stay exactly equal while the two objects fly apart at wildly different rates?
  4. Common mistakeWhy don't the equal and opposite forces in a Newton's third law pair cancel each other?
Your turneasy1 of 3
A therapist pushes a 75 kg patient on a frictionless sled, producing a steady acceleration of 4 m/s2. Find the net force on the sled and patient.

4A. Friction, Static and Kinetic

  1. How it worksHow does the normal force set the ceiling on how hard static friction is willing to push back?
  2. Worked exampleFind the largest static friction available on a 25 kg crate on a floor with a coefficient of 0.40.
  3. Common mistakeWhy isn't friction stronger on a box with more of its surface touching the floor?
  4. Going furtherWhat changes about the friction on a block the moment the floor beneath it starts to tilt?
Your turneasy1 of 3
A 31 kg crate rests on a level floor whose coefficient of static friction is 0.524. Using g = 10 m/s2, find the largest friction force the floor can supply before the crate breaks loose.

4A. Inclined Planes and Center of Mass

  1. How it worksHow does weight on a slope break into one piece sliding along the ramp and one pressing into it?
  2. Worked exampleFind the acceleration of a frictionless block released on a ramp tilted 30 degrees.
  3. How it worksHow does a diver's center of mass keep sailing along a smooth arc while the body tucks and spins?
  4. Going furtherWhat happens to a standing person's stability once their center of mass drifts past their toes?
Your turneasy1 of 3
A frictionless block is released on a ramp tilted so that the sine of the incline angle is 0.618. Using g = 10 m/s2, find the block's acceleration down the slope.

4A. Translational Equilibrium and Force Balance

  1. How it worksHow does setting the horizontal and vertical force sums to zero pin down two unknown tensions?
  2. Worked exampleFind the tension in two symmetric cables angled 40 degrees that hold a 200 N traction weight.
  3. Common mistakeWhy isn't an object in equilibrium necessarily an object sitting still?
Your turnmedium1 of 3
A 151 N weight hangs at rest from a rope while a horizontal cord pulls it aside, holding the rope at an angle to the vertical whose tangent is 0.654. Find the tension in the horizontal cord.

4A. Torque, Lever Arms, and Rotational Equilibrium

  1. How it worksHow does the perpendicular distance from the pivot to the line of the force set the torque?
  2. How it worksWalk me through why yanking a wrench straight along its own handle turns the bolt not at all.
  3. Worked exampleFind the torque of a 40 N pull applied 0.25 m from a pivot at 60 degrees to the handle.
  4. Common mistakeWhy isn't torque just the force multiplied by the full length of the thing you push on?
  5. Worked exampleFind where a 600 N worker must stand on a 4 m plank so both end supports carry the same load.
Your turnmedium1 of 3
A 48 N pull is applied to a wrench at a distance of 0.46 m from the bolt, at an angle to the handle whose sine is 0.859. Find the torque about the bolt.

4A. Work, Mechanical Advantage, and the Work-Energy Theorem

  1. How it worksHow does only the part of a force lined up with the motion survive into W equals Fd cos theta?
  2. How it worksHow does a pulley trade a much longer rope pull for a much smaller force at the same total cost?
  3. Worked exampleFind the work done by a 120 N rope dragging a sled 6 m while angled 25 degrees above the ground.
  4. Worked exampleFind the final speed of a 2 kg cart that starts at rest and absorbs 30 J of net work.
  5. Ties togetherHow does the work-energy theorem become the same accounting a muscle burning glucose has to obey?
Your turneasy1 of 3
A rope drags a sled 9 m along level ground with a force of 144 N, the rope held at an angle to the ground whose cosine is 0.92. Find the work done by the rope.

4A. Kinetic Energy and Potential Energy

  1. How it worksHow does raising a mass bank energy in the gravitational field and pay it back on the way down?
  2. Worked exampleFind the kinetic energy carried by a 70 kg sprinter moving at 10 m/s.
  3. How it worksHow does squeezing a spring store energy that climbs with the square of the squeeze?
  4. Worked exampleFind the elastic energy stored in a spring of stiffness 200 N/m compressed by 0.10 m.
  5. Common mistakeWhy isn't gravitational potential energy something an object owns all by itself?
Your turneasy1 of 3
Find the kinetic energy carried by a 78 kg sprinter running at 9 m/s.

4A. Conservation of Energy, Conservative Forces, and Power

  1. How it worksHow does a roller coaster keep trading height for speed while the total energy never moves?
  2. Worked exampleFind the speed of a 0.50 kg ball at the bottom after it falls 1.8 m from rest.
  3. How it worksHow does a conservative force return every joule it took no matter which path you wandered?
  4. Worked exampleFind the power output of a 60 kg climber who rises 3.0 m of stairs in 4.0 seconds.
  5. Going furtherWhat happens to the energy ledger when a sled slides to a dead stop on rough snow?
Your turneasy1 of 3
A ball is released from rest and falls 9 m. Using g = 10 m/s2 and neglecting air resistance, find its speed on arrival.

4A. Periodic Motion: Amplitude, Frequency, and Phase

  1. How it worksHow do amplitude, frequency and phase each deform a sine curve in a completely different way?
  2. Worked exampleFind the period and the frequency of a 0.25 kg mass on a spring of stiffness 100 N/m.
  3. How it worksHow does a mass on a spring swap kinetic and potential energy twice in every single cycle?
  4. Common mistakeWhy doesn't hauling a pendulum farther back make each swing take longer?
Your turneasy1 of 3
A mass on a spring completes 44 full oscillations in 10 s. Find the frequency of the motion.

4A. Transverse and Longitudinal Waves

  1. How it worksHow do transverse and longitudinal waves shake their particles in completely different directions?
  2. How it worksHow do wavelength, frequency and propagation speed lock together into v equals f lambda?
  3. Worked exampleFind the wavelength of a 256 Hz tone travelling through air at 343 m/s.
  4. Going furtherWhat happens to a wave's frequency and its wavelength when it crosses into a stiffer medium?
Your turneasy1 of 3
A sound wave has a frequency of 687 Hz and a wavelength of 1.24 m. Find its propagation speed.

AP®, SAT® and PSAT/NMSQT® are trademarks registered by the College Board (PSAT/NMSQT® jointly with the National Merit Scholarship Corporation). ACT® is a registered trademark of ACT Education Corp. GRE® is a registered trademark of ETS. LSAT® is a registered trademark of the Law School Admission Council. MCAT® is a registered trademark of the Association of American Medical Colleges. ISEE® and SSAT® are registered trademarks of their owners. None of these organizations is affiliated with, or endorses, Jentoo.