Physics Ninja: Mastering Impulse, Momentum, and Collisions

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.