-
Please find my solutions to past F=ma Contest problems below. Past Exams Problems organized by topic Quarter-final Exams Problems organized by topic
-
Topic: CollisionsConcepts: 1D elastic collision, Energy dissipation Solution: By conservation of energy, the velocity of m1m_1 when it reaches m2m_2 is Using the elastic collision equation, the velocity of m2m_2 right after the collision is We conserve energy again to find how far m2m_2 slides: so the answer is B.
-
Topic: Rigid BodiesConcepts: Conservation of energy, General kinetic energy, Rolling motion Solution: Since the ball rolls without dissipation, we know it is rolling without slipping: Conserving energy between the top and bottom of the ramp, Using I=25MR2I=\frac{2}{5}MR^2 and v=Rωv=R\omega, When the ball is launched vertically, only the translational kinetic energy gets converted to gravitational potential
-
Topic: EnergyConcepts: Kinetic energy, Projectile motion Solution: By definition of kinetic energy, where vxv_x is the initial horizontal velocity of the ball. Since the ball is undergoing projectile motion, its horizontal velocity stays constant. After time tt, its vertical velocity is We are given the kinetic energy at this point is 3K3K so we have
-
Topic: DynamicsConcepts: Forces in mechanics, Statics Solution: Since the left and right mass are at rest, we have Then we have 3 forces of equal magnitude acting on the middle mass. Since it is also at rest, this means the forces are equally spaced by angle. Thus, the angle between the two ropes is 2π/32\pi/3.
-
Topic: DynamicsConcepts: Newton’s laws Solution: Applying Newton’s 2nd law to the lower block, we have Recall kinetic friction is given by f=μNf=\mu N so Substituting into the first equation, so the answer is A.
-
Topic: DynamicsConcepts: Newton’s laws Solution: Applying Newton’s 2nd law, we have in the vertical direction, In the horizontal direction, Substituting in the first equation, so the answer is C.
-
Topic: DynamicsConcepts: Forces in mechanics, Inclined plane Solution: The car uses static friction to accelerate up the hill. By Newton’s 2nd law, To maximize acceleration, we take the maximum value of static friction, so the answer is B.
-
Topic: DynamicsConcepts: Angular momentum, Circular motion Solution: Recall the centripetal acceleration is given by and the angular momentum is given by When Harry passes out, we have ac=5ga_c=5g which yields so the answer is D.
-
Topic: KinematicsConcepts: Projectile motion Solution: Recall from projectile motion the range and height equations, Then so the answer is E.
-
Topic: KinematicsConcepts: Projectile motion Solution: Recall from projectile motion that the y-component of a particle’s velocity flips direction when the particle returns to its starting height. Applied to our case, the particle thrown upwards returns to the height of the ledge with the same velocity as the particle thrown downwards. Thus, the difference in time
-
Topic: KinematicsConcepts: Free fall Solution: The time taken for the piano to drop from rest at h1h_1 to the ground is The time taken for the piano to drop from rest at h1h_1 to h2h_2 is Thus, the time taken for the piano (released at h1h_1) to drop from h2h_2 to the ground is so
-
Topic: KinematicsConcepts: Motion graphs Solution: In a position-time plot, speed is given by the magnitude of the slope of the graph. In our case, the squirrel travels at three different speeds over its motion. Part II has the largest magnitude of slope corresponding to time B to D. Thus, the answer is C. Topic: KinematicsConcepts:
-
Topic: Rigid BodiesConcepts: Angular kinematics, Rotational Newton’s 2nd law Solution: Since both discs come to rest, they go to rest at the same time. From angular kinematics, so the quantity ω/α\omega/\alpha is the same for both disks: Let’s rewrite α\alpha in terms of rr. We have using the fact that τ∝r\tau \propto r as the
-
Topic: DynamicsConcepts: Inclined plane, Statics, Torque from weight Solution: Recall the slip angle on an inclined plane is given by To find the tip angle, note that when the block is about to tip over, the only point in contact with the plane is the bottom corner. If we choose this as our pivot point,
-
Topic: Oscillatory MotionConcepts: Mass-spring system, Power Solution: Recall the instantaneous power delivered to the mass is P=FvP=Fv where FF is the spring force and vv is the velocity of the mass. Thus, power delivered is first maximized at t=3T/8t=3T/8 so the answer is D.
-
Topic: GravityConcepts: Gravitational potential energy Solution: Recall the gravitational potential energy between two masses MM and mm separated by distance rr is In our case, we have so the answer is D. Topic: GravityConcepts: Center of mass, Circular orbits Solution: The gravitational force FF on 3M3M is given by This provides the centripetal acceleration so
-
Topic: CollisionsConcepts: Conservation of linear momentum Solution: Conserving momentum in the x-direction, Conserving momentum in the y-direction, By the Pythagorean theorem, so the answer is C.
-
Topic: KinematicsConcepts: Projectile motion Solution: Recall from projectile motion the range and height equations, To maximize the range, θ=π/4\theta=\pi/4 which yields R(π/4)=v2/gR(\pi/4)=v^2/g and H(π/4)=v2/4gH(\pi/4)=v^2/4g. In our case, we have so Thus, the answer is B.
-
Topic: Oscillatory MotionConcepts: Simple pendulum Solution: Recall the period of a simple pendulum is given by In our system, the pendulum oscillates as a simple pendulum of length LL half the time and as a simple pendulum of length L/3L/3 half the time. Thus, the period is so the answer is E.
-
Topic: OtherConcepts: Dimensional analysis Solution: Thus, the answer is D.
F=ma Training Program
Group (2026)
Individual (2026)
- Announcements (2)
- F=ma Exam (527)
- Kalda (98)
- Kinematics (34)
- Mechanics (54)
- Relativity (10)
- Miscellaneous (9)
- Morin (92)
- Physics (8)
- Quarter-Final Exam (9)
- Townsend (5)
- Chapter 9 (5)
- USAPhO (61)
- May 2024
- April 2024
- March 2024
- October 2023
- September 2023
- August 2023
- January 2023
- December 2022
- November 2022
- October 2022
- September 2022
- August 2022
- July 2022
- June 2022
- December 2021
- October 2021
- July 2021
- June 2021
- May 2021
- April 2021
- January 2021
- November 2020
- October 2020
- September 2020
- August 2020
- March 2020
- December 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- February 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- January 2017
- October 2016
- September 2016
- August 2016
- July 2016
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
You must be logged in to post a comment.