Kevin S. Huang

  • F=ma Exam Solutions

    Please find my solutions to past F=ma Contest problems below. Past Exams Problems organized by topic Quarter-final Exams Problems organized by topic

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  • 2009: Problem 16

    Topic: Oscillatory MotionConcepts: CM frame, Effective spring constant, Mass-spring system Solution: We go to the CM frame, where both masses oscillate about their midpoint. If we look at one of the masses (the other mass is the mirror reflection), it behaves as a mass-spring system with a half-spring. Since cutting a spring in half doubles

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  • 2009: Problem 15

    Topic: DynamicsConcepts: Forces in mechanics, Newton’s laws Solution: Since the suitcase is moving at constant velocity, the net force on the suitcase is zero. By Newton’s 2nd law, we have in the horizontal direction and in the vertical direction. Since f=μNf=\mu N, we substitute in the first and second equations: so the answer is C.

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  • 2009: Problem 14

    Topic: CollisionsConcepts: Ballistic pendulum, Conservation of angular momentum, Conservation of linear momentum Solution: Thus, the answer is E.

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  • 2009: Problem 13

    Topic: DynamicsConcepts: Statics, Torque Solution: If the fulcrum was at Henry, we wouldn’t have static equilibrium since Lucy is heavier than Mary and they both have the same moment arm. Thus, the fulcrum should be between Henry and Lucy. Balancing torques, Thus, Lucy exerts the most torque so the answer is B.

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  • 2009: Problem 12

    Topic: EnergyConcepts: Gravitational potential energy, Work-energy theorem Solution: Batman does work to increase his own gravitational potential energy by MghMgh. Then he does work to increase Robin’s gravitational potential energy by mghmgh. The total work he does is so the answer is C.

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  • 2009: Problem 11

    Topic: EnergyConcepts: Motion graphs, Work Solution: Recall work is given by the position integral of the force, Using Newton’s 2nd law, which is the product of mass and the signed area under the aa–xx plot. Thus, so the answer is A.

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  • 2009: Problem 10

    Topic: KinematicsConcepts: 5 kinematics equations, Free fall Solution: From kinematics, the trajectory of the first apple is The trajectory of the second apple is The displacement between the two apples is then At t=2st=2\,\mathrm{s}, we have so the answer is C.

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  • 2009: Problems 8-9

    Topic: KinematicsConcepts: Angular kinematics, Motion graphs Solution: Since angular acceleration α\alpha is the time derivative of the angular velocity ω\omega, we can determine α\alpha from a ω\omega–tt plot by finding the slope. so the answer is D. Topic: KinematicsConcepts: Angular kinematics, Motion graphs Solution: The area under a ω\omega–tt plot gives the angular displacement Δθ\Delta\theta.

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  • 2009: Problem 7

    Topic: KinematicsConcepts: 5 kinematics equations Solution: We use the kinematics equation without the time variable, The acceleration is so the answer is B.

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  • 2009: Problem 6

    Topic: KinematicsConcepts: Conservation of energy, Projectile motion Solution: By conservation of energy, we have vv is independent of α\alpha so the answer is C.

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  • 2009: Problem 5

    Topic: GravityConcepts: Circular orbits, Conservation of angular momentum, Elliptical orbits Solution: By conservation of angular momentum, each satellite has the same angular momentum at any point along its orbit. Thus, we can shift point A to coincide with the apogee of the ellipse and point C to coincide with the perigee of the ellipse. Recall

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  • 2009: Problem 4

    Topic: DynamicsConcepts: Newton’s laws Solution: The force of the spaceman on the spacecraft is equal to the normal force on the spaceman. By Newton’s 2nd law, we have Since we are given a=5ga=5g, so the answer is A.

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  • 2009: Problems 2-3

    Topic: CollisionsConcepts: 1D elastic collision Solution: Recall that in an elastic collision between identical masses, if a moving mass hits a mass at rest then the velocity of the moving mass is transferred to the second mass. If two masses move toward each other with the same speed, then their directions flip after the collision.

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  • 2009: Problem 1

    Topic: CollisionsConcepts: Conservation of energy, General Newton’s 2nd law Solution: By conservation of energy, the velocity of the apple right before it hits the ground is By Newton’s 2nd law, the average force exerted on the apple is since the apple comes to rest. The average pressure is then so the answer is B.

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  • 2008: Problem 25

    Topic: GravityConcepts: Circular orbits, Elliptical orbits Solution: Recall for the circular orbit, we have For the elliptical orbit, the starting point is the apogee so using our results for elliptical orbits (note b2=a2−c2b^2=a^2-c^2). Substituting these into the first equation, We have so the answer is E.

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  • 2008: Problem 24

    Topic: KinematicsConcepts: 1D inelastic collision, Free fall Solution: If a ball is launched upward with velocity vv, then it will reach the top in time The ball takes the same amount of time to come down so the time for the first bounce is For the second bounce, the velocity is modified by a factor

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  • 2008: Problem 23

    Topic: GravityConcepts: Escape velocity, Gravitational force, Kepler’s laws Solution: Thus, the answer is C.

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  • 2008: Problem 22

    Topic: CollisionsConcepts: Ballistic pendulum, Circular motion, Forces in mechanics Solution: By conservation of linear momentum, We conserve energy between the bottom and top of the vertical circle, The minimum velocity at the top of the vertical circle is attained when the tension in the string goes to zero. Only gravity provides the centripetal acceleration so

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  • 2008: Problem 21

    Topic: System of MassesConcepts: Conservation of linear momentum Solution: Thus, the answer is B.

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  • 2008: Problem 20

    Topic: OtherConcepts: Limiting cases, Young’s modulus Solution: Eliminate: Thus, the answer is D.

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1D elastic collision 1D inelastic collision 5 kinematics equations Air resistance Angular kinematics Angular momentum Artificial gravity Atwood machine Average vs. instantaneous Ballistic pendulum Bernoulli's principle Buoyant force Center of mass Circular motion Circular orbits CM frame Conservation of angular momentum Conservation of energy Conservation of linear momentum Coriolis force Data expression Dimensional analysis Dynamics Dynamics of CM Effective spring constant Elliptical orbits Energy dissipation Equivalence principle Error propagation Escape velocity Fictitious forces Floating Fma: Collisions Fma: Dynamics Fma: Energy Fma: Fluids Fma: Gravity Fma: Kinematics Fma: Oscillatory Motion Fma: Other Fma: Rigid Bodies Fma: System of Masses Forces in mechanics Free fall Gauss's law for gravity General angular momentum General kinematics equations General kinetic energy General Newton's 2nd law Gravitational force Gravitational potential energy Impulse-momentum theorem Inclined plane Kepler's laws Kinematics Kinetic energy Law of reflection Limiting cases Mass-spring system Mechanics Moments of inertia Motion graphs Newton's laws Parallel-axis theorem Pascal's law Perpendicular-axis theorem Physical pendulum Potential energy graphs Power Pressure with depth Projectile motion Pulleys with rotational inertia Qtrfin: E&M Qtrfin: Mechanics Recursion for rotational inertia Reduced mass Relative velocity Rigid Bodies Rolling down inclined plane Rolling motion Rotational Newton's 2nd law Scale reading Simple harmonic motion Simple pendulum Small angle approximation Speed vs. velocity Spring potential energy Statics Surface tension Tensile strength Torque Torque from weight Types of equilibrium Vectors Velocity constraints Vertical spring Wave speed in string Work Work-energy theorem Young's modulus