PH2105 Mechanics - Lecture 9: Momentum & Collisions

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Questions and Answers

How does momentum behave in relation to an object's mass and velocity?

Momentum depends solely on an object's mass.

Momentum depends solely on an object's velocity.

Momentum is dependent on the object's shape and air resistance.

Momentum is influenced equally by an object's mass and velocity. (correct)

Which of the following correctly relates force and momentum according to Newton's second law?

Force is the rate of change of momentum. (correct)

Force is proportional to the square of momentum.

Force is independent of momentum and velocity.

Force decreases as momentum increases.

What happens to the change in momentum if a force is applied for twice as long?

The change in momentum doubles. (correct)

The change in momentum remains the same.

The change in momentum reduces by half.

The object's momentum becomes negative.

What are the SI units of impulse?

N s Signup and view all the answers

How are the momenta of an air molecule and an automobile compared?

The momentum of the automobile differs by 27 orders of magnitude. Signup and view all the answers

What is the proper definition of linear momentum?

The product of mass and velocity. Signup and view all the answers

Which statement accurately describes the relationship between impulse and momentum?

Impulse is directly related to the change in momentum. Signup and view all the answers

Why is conservation of momentum particularly important in the study of collisions?

It helps predict the velocities after the collision. Signup and view all the answers

Which of the following units is not a unit for measuring momentum?

J Signup and view all the answers

What does the center of mass refer to?

The point at which all the mass of a body can be considered to concentrate. Signup and view all the answers

Which of the following is true about momentum as a vector quantity?

It can be negative when an object moves backward. Signup and view all the answers

Which scenario describes an elastic collision?

A ball bounces off a wall without losing speed. Signup and view all the answers

What is the implication of a system having a conserved energy?

Energy can change forms but cannot be created or destroyed. Signup and view all the answers

What characterizes an elastic collision?

Kinetic energy is conserved. Signup and view all the answers

In a completely inelastic collision, what happens to the colliding bodies?

They stick together and move as one mass. Signup and view all the answers

If two bodies experience a collision and external forces are negligible, what happens to the total momentum?

It remains constant. Signup and view all the answers

What is the implication of having a center of mass in a system of particles?

It helps to determine the motion of the entire system. Signup and view all the answers

When a dropped ball sticks to the ground and does not bounce back, this is an example of which type of collision?

Inelastic collision. Signup and view all the answers

In the described car crash scenario, which of the following is required to determine the wreckage's velocity post-impact?

Initial speeds and masses of both vehicles. Signup and view all the answers

What happens to the total kinetic energy in an elastic collision compared to an inelastic collision?

Total kinetic energy is conserved in an elastic collision, but not in an inelastic collision. Signup and view all the answers

Which of the following statements about momentum is true when two objects collide elastically?

Momentum is conserved. Signup and view all the answers

Which method results in the greater impulse of the net force on the car?

Impulse is the same in both cases Signup and view all the answers

What must be true for the total momentum of a system to be conserved?

External forces acting on the system must be zero Signup and view all the answers

According to Newton's Third Law, what can be said about the forces between two interacting particles?

The forces are equal in magnitude and opposite in direction Signup and view all the answers

What is the key principle behind the conservation of momentum?

Total momentum remains constant if external forces sum to zero Signup and view all the answers

When a car comes to a sudden stop by slamming into a wall, what can be concluded about its change in momentum?

It is equal to the change in momentum when stopping gradually Signup and view all the answers

What effect does a gradual stop have on the forces acting on a car compared to a sudden stop?

The forces acting are more sustained and less intense over time Signup and view all the answers

In the conservation of momentum scenario with two isolated particles, what happens to the momentum when they interact?

Momentum is exchanged but total momentum remains constant Signup and view all the answers

When considering the impulse of net force during a collision, what does impulse represent?

The area under the force-time graph Signup and view all the answers

What does the impulse-momentum theorem state about the relationship between impulse and momentum?

Impulse is equal to the change in momentum during a time interval. Signup and view all the answers

In the context of impulse, what does the area under the curve on a graph of $\Sigma F_x$ versus time represent?

The impulse experienced by the object. Signup and view all the answers

If a ball of mass 0.40 kg changes its velocity from -30 m/s to +20 m/s after colliding with a wall, what is the impulse of the net force on the ball?

20 Ns Signup and view all the answers

Which condition affects the change in momentum of a particle?

The time interval over which the net force acts. Signup and view all the answers

In the case of a soccer ball initially traveling at 20 m/s to the left and then kicked to 30 m/s at a 45° angle, what determines the impulse imparted to it?

The time duration of the collision and the change in velocity. Signup and view all the answers

What is the mathematical expression for impulse as described in the content?

$J = \Sigma F \Delta t$ Signup and view all the answers

How does the impulse of a net force during a collision correlate with the change in momentum for an object?

Impulse equals the change in momentum for the time the force is applied. Signup and view all the answers

Which statement accurately describes the difference between momentum and kinetic energy?

Momentum depends on time of net force application, while kinetic energy depends on distance. Signup and view all the answers

What does Newton’s Second Law imply about the forces acting on two objects A and B in terms of their momentum?

The total momentum remains constant in the system. Signup and view all the answers

Under what condition is momentum conserved in a collision according to the conservation of momentum principle?

When the vector sum of external forces on the system is zero. Signup and view all the answers

Which statement about the principle of conservation of momentum is correct?

It is derived from Newton’s Third Law. Signup and view all the answers

In a situation where a spring-loaded toy breaks into three pieces, if pieces A and B move in negative directions, what can be inferred about piece C's velocity components?

The components must balance the momentum of A and B. Signup and view all the answers

What are the signs of the velocity components of Piece C if Piece A moves in the negative x-direction and Piece B moves in the negative y-direction?

vC-x > 0 and vC-y < 0 Signup and view all the answers

What is the result of the total momentum in an isolated system as suggested by Newton's principles?

Total momentum remains constant. Signup and view all the answers

What assumption is crucial for the conservation of momentum to hold true?

The system must be closed and isolated. Signup and view all the answers

How does momentum conservation relate to Newton’s Third Law?

Momentum conservation is directly due to equal and opposite reactions. Signup and view all the answers

Study Notes

PH2105 Mechanics - Lecture 9: Momentum, Impulse & Collisions

Lecturer: Dr Ayesha Sharif
Date: November 6th, 2024
Topics Covered:
- Linear momentum
- Impulse (relationship to force and change in momentum)
- Conservation of linear momentum
- Collisions
- Centre of mass
Textbooks: OpenStax - Chapter 9, Young and Freedman - Chapter 8
Introduction:
- The concepts of impulse, momentum, and centre of mass are critical for success in major-league sports (e.g., baseball).
- Misjudging these concepts can lead to damage (e.g., a broken bat).
- Concepts of work, energy, and the work-energy theorem are powerful tools for analyzing complex physical systems.
- The total energy of a closed system is conserved.
- Defining another conserved quantity, linear momentum, along with the impulse-momentum theorem, adds additional constraints to how a system evolves over time, useful for understanding collisions.
Linear Momentum:
- Linear momentum (p) of a particle is defined as p = mv.
- Momentum is a vector quantity with S.I. units of kg m/s.
- Momentum can be understood as "mass in motion".
- The velocity and momentum vectors for an object are in the same direction.
- Momentum depends equally on mass and velocity.
- Momenta of different objects can differ significantly in magnitude (e.g., air molecule vs. car)
Momentum and Newton's Second Law:
- Newton's Second Law can be written as ΣF = (mv)/dt.
- Momentum (p) is a vector with the same direction as velocity.
- Force and momentum are vectors; their components obey similar equations.
- Newton's second law can be written in terms of momentum: ΣF = dp/dt.
Impulse:
- Change in momentum of an object is proportional to the length of time the force is applied.
- A larger force results in a larger change in momentum.
- Impulse (J) of a force is the product of the force and the time interval during which it acts.
- J = ΣF * Δt = change in momentum (Δp).
- Impulse is equal to the area under a force vs. time graph.
Impulse-momentum Theorem:
- The change in momentum of a particle during a time interval is equal to the impulse of the net force acting on the particle during that interval.
- If the net external force on a system is zero, the total momentum of the system is conserved.
Comparison of Momentum and Kinetic Energy:
- Kinetic energy is equal to the work done on the object.
- Momentum is equal to the impulse on a body.
- Changes in momentum depend on time over which net force acts.
- Changes in kinetic energy depend on the distance over which the force acts.
Conservation of Momentum:
- External forces acting on a system but their vector sum = zero
- The total momentum of the system is conserved.
- This principle applies when dealing with isolated systems, where no external forces are present.
Principle of Conservation of Momentum:
- Momentum is conserved during a collision.
- Assuming no external forces, the momentum of an isolated system is constant.
- Applicable to more than two particles.
Center of Mass:
- Restating momentum conservation using the concept of center of mass. A useful concept.
- For multiple particle systems, define the center of mass with its position vector.
Center of Mass of Symmetrical Objects:
- The geometrical centre can be used to locate the centre of mass of symmetrical objects.
- Centre of mass on axis of symmetry for an object.
- Centre of mass does not always need to be within the object.
Problem Examples:
- Provided examples include car crash and elastic straight-line collision problems, illustrating applications of momentum and impulse principles.

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Explore the fundamental concepts of momentum, impulse, and collisions in this quiz based on PH2105 Mechanics Lecture 9. You'll dive into the relationships between linear momentum, impulse, and conservation principles, essential for understanding complex systems. Prepare to test your knowledge of key concepts that underpin many physical phenomena.