2022 Live Review 4 | AP Physics C: Mechanics | System of Particles and Linear Momentum

Julie Hood from Mast Academy High School introduces the AP Physics C Mechanics live review session, focusing on linear momentum and impulse. The session will cover the relationship between mass, velocity, and momentum, the role of force over time in collisions, and changes in momentum and kinetic energy. Julie suggests using resources from the College Board's website for practice, emphasizing the importance of understanding expectations for the exam. She introduces the concept of momentum as a conserved vector quantity and the impact of external forces on it.

The script explores a scenario involving a truck and a car with identical engines, discussing kinetic energy and momentum. It explains that despite different finishing times in a race, both vehicles end with the same kinetic energy due to the same work done by the constant force. However, the truck, taking longer to finish, has more momentum due to the time factor in momentum change calculations. The script also considers the kinetic energy and momentum during the race, concluding that the smaller car has more kinetic energy mid-race due to its higher velocity.

This section delves into collision problems, using the conservation of momentum principle. It presents a problem where two discs of different masses and velocities collide and stick together, resulting in a composite body with a velocity that can be calculated using conservation of momentum. Another example involves a cannon firing a projectile, which comes to rest while the projectile continues moving, illustrating the application of conservation of momentum in determining the projectile's velocity.

The script explains how to use force-time graphs to calculate changes in momentum, emphasizing the integral of force over time as the area under the curve. It provides an example where a variable force acts on an object, and the total change in momentum is found by adding the areas of rectangles under the graph, resulting in a net change of zero. The section also touches on using calculus for non-linear force functions to find momentum changes.

This part of the script discusses the vector nature of momentum, emphasizing the importance of direction in momentum calculations. It presents a problem involving a collision and the subsequent vector addition of momenta to determine the correct set of vectors representing the momenta after the collision. The script also addresses a scenario where a ball collides with the floor and rebounds, explaining how to determine the impulse exerted by the floor using vector subtraction.

The script introduces the concept of explosions as a type of problem where internal forces are involved, and momentum is conserved despite the system's internal changes. It presents a problem involving a mass that explodes into two pieces with specific mass ratios and velocity changes, using algebra to find the velocity of the resulting pieces. Another problem involves a projectile that explodes at its highest point, with one piece falling straight down and the other moving horizontally, illustrating the application of conservation of momentum in two dimensions.

This section focuses on projectile motion and collision analysis, starting with a dart launched at an angle that collides with a hanging block at the peak of its trajectory. The collision is inelastic, and the script explains how to use conservation of momentum to find the velocity of the combined dart-block system. It then calculates the height reached by the system using energy conservation and explores the effect of a more massive dart on the collision outcome and the period of oscillation.

The final paragraph wraps up the session by summarizing key points about linear momentum, impulse, and their applications in various problems, including explosions and collisions. It emphasizes the importance of understanding momentum conservation and the impact of external forces. The script encourages students to review past exams, free response questions, and scoring rubrics for deeper understanding and to prepare for the upcoming review on torque and rotational kinematics.