Chapter 7: Laws of Motion and Momentum

Question 1

What is Newton’s First Law?

Answer 1

• Newton’s First Law states that an object wil remain at rest or continue to move with constant velocity unless acted upon by a resultant force.
  
  • If an object’s velocity changes, then a resultant force must be acting on it.

Question 2

1. What is Newton’s Second Law?
2. How can the equation F = Δp / Δt be derived?
3. How can the equation F = ma be derived?

Answer 2

1. Newton’s Second Law states that the net (resultant) force acting on an object is directly proportional to the rate of change of its momentum, and is in the same direction.
2. Image below.
3. Image below.

Question 3

What is Newton’s Third Law?

Answer 3

Newton’s Third law states that when two objects interact, each object exerts an equal but opposite force on the other object during the interaction. So all forces in the universe occur in equal but oppositely directed pairs.

Question 4

The opposing forces in a particular interaction always have the same fundamental force. All interactions can be explained in terms of the four fundamental forces of nature.

Describe these forces.

Answer 4

• Graviational and electromagnetic interactions produce long-range forces which are observed in daily life.
• Strong and weak interactions produce extremely short-ranged forces. These are responsible for nuclear forces.

Question 5

By considering individual forces in an isolated system, explain why it is not possible for an isolated system to exert a net force on itself.

Answer 5

• Consider forces inside an isolated system.
• In this case, a force on one part of the system will be countered by an equal and opposite force on another part of the system.
• Therefore, an isolated system cannot exert a net force on the system itself: it requires an interaction with an external object to produce a net force and, hence, an acceleration.

Question 6

1. Define linear momentum.
2. What are its units?
3. Why is momentum a vector quantity?

Answer 6

1. The linear momentum p of an object depends on its mass and velocity.
   momentum = mass x velocity
2. The SI unit of momentum is kg m s^-1.
3. Momentum is a vector quantity because it is a product of a scalar (mass) and a vector (velocity).

Question 7

1. Describe the principle of conservation of momentum.
2. How can the principle be used to predict the motion of interacting objects?

Answer 7

1. The principle of conservation of momentum states that, for a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system.
2. The principle can be used to predict the motion of interacting objects as it implies that the total momentum before and after the collision is equal.

Question 8

A gun recoils when a bullet is fired. Comment on the momentum of this system.

How can this be applied to smaller and larger forces?

Answer 8

A gun recoils when a bullet is fired. The total momentum of this system remains the same and is equal to zero. The momentum of the gun and the momentum of the bullet have the same magnitude but act in opposite directions.

The same physics can be used to explain a recoiling radioactive nucleus when it emits an alpha-particle, and an exploding firework.

Question 9

Compare perfectly elastic and inelastic collisions.

Answer 9

• Momentum and total energy is conserved in all collisions.
• However, perfectly alastic collisions conserve kinetic energy whereas inelastic collisions do not conserve kinetic energy as it is transformed into other forms such as heat.

Question 10

Describe two methods to investiagte momentum in the laboratory. Which is better, why?

Answer 10

There are several ways to investigate momentum in the laboratory.

• A linear air track is ideal because it minimises the friction between gliders and the track, but trolleys and a horizontal runway can also be used.
  
  • The velocity of each object is determined with a motion sensor and a laptop; light gates and a digital timer; ticker timers; or simply a stopwatch to measure the time taken to cover a known distance.

Question 11

1. Define impulse.
2. Compare this to Newton’s Second Law.
3. What units are used for impulse?

Answer 11

1. The impulse of a force is defined as force x time.
2. As per Newton’s Second Law, the change in momentum is also equal to force x time [F x Δt = Δp]. Therefore the impulse of a force = change in momentum.
3. Impulse is measured in N s or kg m s^-1.

Question 12

How can impulse be calculated from a graph?

Answer 12

As impulse = force x time, the area under a force-time graph is equal to the impulse of a force/change in momentum. For non-linear graphs, the area under the graph can be estimated by splitting it into regular shapes.

Question 13

The figure below shows a general collision involving two objects of mass m₁ and m₂. The white object travels at velocity v₀ and collides with the stationary black objects. After the collision, the white object travels at angle θ₁ to its original direction with velocity v₁, and the black object travels at angle θ₂ with velocity v₂.

Derive an equation for the x- and y-direction momenta using the principle of conservation of momentum.

Answer 13