AP Physics C Mechanics Unit 4: Linear Momentum 4.3 Conservation of Linear Momentum Ms. Shamsa Period 1 10 February 2025 Essential Knowledge: Learning Objective: • A Describe the behavior of a system using conservation of linear momentum. • Describe how the selection of a system determines whether the momentum of that system changes Success Criteria: - Calculate the position, velocity and acceleration of system’s center of mass. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Engage Think –pair-Share why the gun recoils when a bullet is fired from it Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Conservation of linear momentum states that the total linear momentum of a closed system remains constant unless acted upon by an external force. It is also closely related with the principle of action and reaction which states that for every action there's an equal and opposite reaction. This law of conservation can also be written as: 𝑝𝑓 =𝑝𝑖 Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. The initial momentum is equal to the final momentum, if there was no impulse. Δp = 0 𝑝𝑖 = 𝑝𝑓 For system of two objects 𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖 = 𝑚1 𝑣1𝑓 + 𝑚2 𝑣2𝑓 Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Center of mass (COM) is the point in an object or system where the total mass is considered to be concentrated. The center of mass, also called center of gravity, for a collection of particles is the average position of the particles, weighted according to their relative masses. Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes The position of the system's center of mass Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. The same procedure applies to systems containing more than two objects Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. If the objects within a system are moving, then the system’s center of mass may be moving too Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Center of mass acceleration The acceleration of COM can be found by taking the derivative of its velocity with respect to time. This will give the acceleration of the COM. Conservation of momentum tells us that if a system experiences zero net external force, the total momentum of the system, does not change. Therefore, if a system experiences zero net external force, the equation above tells us that doesn't change either. The velocity of a system’s center of mass is constant in the absence of net external forces Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. • A system’s p remain constant, when only internal forces act. You can always choose some system in which p remains constant. • The center of mass is the location that behaves as if all the system’s mass were concentrated there • The center of mass position, velocity and acceleration each relate to the weighted average • Momentum of the system will be Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Mass 𝑚1 is moving with speed v toward stationary mass 𝑚2 . The speed of the center of mass of the system is Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Mass 𝑚1 is moving with speed v toward stationary mass 𝑚2 . The speed of the center of mass of the system is Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Option E The definition of the center of mass velocity is the total momentum divided by the total mass Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. • As the system started at rest and the only internal forces on the system • COM of the system must remain stationary. • When the person walks to the other side of the boat, it merely flips the system to its mirror image, there the center of the raft is now a distance d to the right of the center of mass of the system. • In effect, the person and the center of the raft switch sides. • So, Raft moved by 2d (Option E) Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. Which of the five lettered points represents the center of mass of the sphere-rod combination? -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. Which of the five lettered points represents the center of mass of the sphere-rod combination? Let A be the origin. 𝑥𝑐𝑚 = [(10 kg)(0) + (5 kg)(L)]/(10 kg + 5 kg) = L/3 Point B Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Two people are initially standing still on frictionless ice. They push on each other so that one person, of mass 120 kg, moves to the left at 2 m/s, while the other person, of mass 80 kg, moves to the right at 3 m/s. What is the velocity of their center of mass? (A) Zero (B) 0.5 m/s to the left (C) 1 m/s to the right (D) 2.4 m/s to the left (E) 2.5 m/s to the right Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Two people are initially standing still on frictionless ice. They push on each other so that one person, of mass 120 kg, moves to the left at 2 m/s, while the other person, of mass 80 kg, moves to the right at 3 m/s. What is the velocity of their center of mass? (A) Zero (B) 0.5 m/s to the left (C) 1 m/s to the right (D) 2.4 m/s to the left (E) 2.5 m/s to the right Option A As the system started at rest and the only forces on the system are between parts of the system, the center of mass must remain stationary Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can -Calculate the position, velocity and acceleration of system’s COM. -Analyze the total momentum of the system remain constant, if net external force on the selected system is zero (conservation of linear momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. . Solve the Assigned related Topic questions on AP Classroom Words of the Day : Conservation of linear Momentum, Center of mass 4.3 Conservation of Linear momentum Evaluate Learning Intention * Describe the behavior of a system using conservation of linear momentum. * Describe how the selection of a system determines whether the momentum of that system changes Success Criteria I Can How would you rate your learning and understanding from today’s lesson Rating 1 2 3 SC1-Calculate the position, velocity and acceleration of system’s COM. SC2-Analyze -Calculate the total momentum of the system remain constant, if the position, velocity and net external force on the selected system is zero (conservation of linear momentum) acceleration of system’s COM. SC3:--Evaluate -Analyze The impulse exerted by one object on a second object the total momentum of the system is equal and opposite to the impulse exerted by the remain constant, if net external second object on the first. force on the selected system is zero (conservation of linear What are my next steps do to understand the learning intentions better and make me a good learner? momentum) -Evaluate The impulse exerted by one object on a second object is equal and opposite to the impulse exerted by the second object on the first. Words of the Day : Conservation of linear Momentum, Center of mass
