Physics Ninja: Mastering Impulse, Momentum, and Collisions

Learn how impulse equals the change in momentum, analyze constant and non-constant force cases, and compute impulse from area under a force–time graph using a tennis ball and racket example.

Compute impulse when the force varies with time by integrating the area under the curve, using rectangles and triangles to sum the area in newton-seconds.

Set average force as a constant over the same delta t to match the impulse; F_avg = impulse / delta t, e.g., 200 N for 1.2 N·s over 6 ms.

Work through six impulse problems—conceptual, graphical, and a two-dimensional case—to reinforce calculating impulse (and momentum) from information or graphs, then download the pdf and compare solutions.

On frictionless ice, Megan (mass M) and Jason (mass 2M) push off from rest, experiencing equal impulse. Megan ends with greater speed because velocity equals impulse divided by mass.

Compute the impulse on an 80 kg sled slowing from 4 to 3 m/s, yielding J = -80 N·s, and the friction force is about -53.3 N over 1.5 s.

Apply the impulse–momentum theorem to a truck of mass 104 with initial velocity 35 m/s. Friction over 2 s brings it to rest, yielding a braking force of 1820 N.

Use conservation of energy to find the velocities before and after impact, then apply impulse equals change in momentum to compute the maximum floor force.

Apply impulse and momentum to a 2 kg object moving at 1 m/s under a 2 N force for 0.5 s. Reach 1.5 m/s to the right.

Compute the impulse from the two-dimensional momentum change for a 0.1 kg baseball, with initial 35 m/s along x and final 17.5 m/s upward, yielding 5.5 kg m/s.

Define a collision system to examine two or more objects and track their combined momentum. Internal forces during collisions conserve the system momentum, even as impulses act on individual momenta.

Explore how two colliding objects conserve momentum, with no external forces, by applying the impulse momentum theorem to each object and to the system as a whole.

Calculate the initial momentum of a two-body system with 5 kg and 8 kg masses moving right and left, showing momentum conservation and equal initial and final momentum.

Conserve momentum on a frictionless ice archer and arrow. A 0.5 kg arrow at 50 m/s causes the archer to recoil about 0.42 m/s in the opposite direction.

Compare elastic, inelastic, and perfectly inelastic collisions, noting momentum conservation in all cases and kinetic energy loss in inelastic events. Learn how sticking objects and external forces influence outcomes.

Perfectly inelastic collisions occur when objects stick together after impact. Use momentum conservation to find the final velocity of the combined mass, noting that kinetic energy is not conserved.

A perfectly inelastic collision involves two particles sticking together; apply conservation of momentum to equate initial and final momentum and determine the direction and magnitude of the combined motion.

Compute the final speed in a perfectly inelastic collision where Bob and the cart move together, using momentum conservation to reach 3 m/s for the 100 kg system.

Apply conservation of momentum to a head-on inelastic collision between an SUV and a car, find the final speed, velocity changes, and energy loss as heat.

Explore how momentum and kinetic energy are conserved in elastic collisions and learn to solve for final velocities using vector direction and sign conventions in a one-dimensional setup.

Examine two-dimensional collisions by applying momentum conservation in the x and y directions. Use vector components and initial and final velocities to analyze elastic and inelastic cases.

this example analyzes a two-dimensional perfectly inelastic collision between a 1500 kg car and a 2500 kg van at an intersection, yielding a speed of 15.6 m/s along resultant momentum.

Analyze a two-dimensional elastic collision between equal-mass billiard balls. Conserve momentum and kinetic energy to relate final speeds and the angles theta and phi, which sum to 90 degrees.

Explore spring properties and collision dynamics where a spring attaches to a block, applying momentum conservation for the quick collision and energy conservation to determine maximum spring compression.

Explore rocket propulsion and thrust through conservation of linear momentum, deriving thrust from ejecting mass, relating it to exhaust speed and changing mass, and applying to problems.

Derivation of thrust and rocket speed using momentum conservation and calculus, showing how exhaust velocity and mass loss drive acceleration and the log-based velocity equation.

Compute rocket acceleration from mass ejection and exhaust speed in one second. Ejecting 1% of mass at 2500 m/s yields about 25 m/s^2, giving about 25 m/s after one second.

Calculate rocket speed using constant mass burn, exhaust velocity, and mass ratio. Apply rocket propulsion equations to determine final velocity from rest.

Explore a variable-mass problem with a cart gaining mass from falling rain, derive the momentum equation, and solve for velocity and acceleration as functions of time, including limiting cases.

Derive final velocities for a one dimensional elastic collision using momentum and kinetic energy conservation; analyze four cases with equal or unequal masses and initial velocities.

Compute the pendulum’s speed at the bottom via energy conservation, then solve a 1d elastic collision with a stationary block using momentum and kinetic energy conservation to find final velocities.

Compare momentum changes for a rubber ball and a clay ball colliding with a wall; show the rubber ball has the larger change and identify momentum units including kg m/s.

Doubling mass and speed yields four times the initial momentum. In an elastic bounce, the momentum's magnitude remains the same while the direction reverses, due to the floor's external force.

Momentum is conserved in an isolated system for elastic or inelastic collisions with no external forces. In the canoe example, zero initial velocity keeps the system stationary, illustrating this conservation.

Analyze momentum conservation in a skateboard scenario to maximize final speed by deflecting the ball, then compare momentum changes in a car-truck collision, noting equal magnitude changes and mass dependence.

Learn that the system’s momentum is conserved in head‑on collisions, while individual objects change momentum; in a rocket explosion, internal forces conserve system momentum.

Analyze collisions between unequal masses to show that impulse equals change in momentum and that equal forces over the same time yield identical impulses, clarifying problems 11 and 12.

Analyze why a falling egg conserves mechanical energy but not momentum under negligible air resistance, and classify a two-block collision as completely inelastic, conserving momentum but not kinetic energy.

This lecture analyzes kinetic energy and momentum, showing that heavier objects with equal kinetic energy have greater momentum, and that doubling momentum makes kinetic energy fourfold.

Tackle the final problem set that blends collisions with conservation of energy, including ballistic pendulum concepts; practice multiple-choice questions, review solutions, and ask questions.

apply the impulse-momentum theorem to stopping times for different masses and analyze a completely inelastic arrow-block collision with momentum conservation, then spring compression to maximum compression.

If two objects share the same momentum, lighter can have greater kinetic energy; released from a compressed spring on a frictionless surface, the objects move oppositely with zero total momentum.

Two football players collide inelastically and stick, yielding a 2 m/s speed in the negative direction, per momentum conservation; an elastic collision with a rubber ball keeps total energy constant.

Examine momentum conservation on a frictionless pond as hammer and student share equal and opposite momentum, while mass differences drive kinetic energy and speed.

Apply momentum conservation to inelastic collisions of railroad cars and rain accumulation in a moving cart, deriving final velocity and kinetic energy, then show rain reduces speed.

Explain momentum conservation in problems: stationary explosion into three pieces and a frictionless sled with drops, deriving the 3m piece velocity as sqrt(2)/3 of the initial velocity, independent of order.

Explore momentum conservation in two-block and two-ball collisions: analyze a perfectly inelastic collision and an elastic two-dimensional collision on a frictionless surface, comparing energy loss and final velocities.

Apply impulse as the area under a force-time graph to determine momentum change, then use momentum conservation to solve a bullet-block collision and compare initial and final kinetic energies.

Problem 17 illustrates work-energy and momentum conservation in a two-mass spring system. Problem 18 covers inelastic collision speed 2/3 v0 and maximum compression x = sqrt(4 m v0^2 /(3 k)).

Calculate momentum components before and after collisions, verify conservation, and analyze kinetic energy changes for sticking collisions, then determine final velocity and maximum spring compression.