Physics: Newton’s Laws and Momentum



Physics: Newton’s Laws and Momentum

Study Guides 18 & 19

Newton’s First law of Motion:

Therefore, if an object is at rest or moving at a constant velocity, the resultant force on it is zero.

Push an object along the ground and it will slow down before coming to rest. This means that it isn’t continuing in its state of ‘uniform motion’. There are two unseen forces, friction and air resistance, that together act on opposition to the motion. As there is no longer a driving force after the object has been pushed, there is resultant backwards force acting on it.

Newton’s Second Law of Motion:

Using what we know about momentum and this definition we can write a useful equation:

If force is equal to rate of change of momentum: F = Δp / Δt

And as momentum is the product of mass and velocity: F = Δ(mv) / Δt

And if mass is constant: F = m (Δv/Δt)

And as rate of change of velocity is acceleration: F = ma

Newton’s Third Law of Motion:

Some examples of Newton’s Third law…

Two skaters glide towards each other; skater A exerts a force on skater B; skater B exerts an equal and opposite force on skater A.

A curling stone, A, moves towards a second curling stone, B, which is at rest. The moving stone, A, exerts a force on B; B, the stone at rest exerts an equal and opposite force on A.

A person standing on the ground; the Earth pulls the person and the person pulls the Earth. Does the Earth accelerate upwards? Yes, it does, but by applying F=ma, the acceleration is minimal because the mass is so great.

Reaction forces are not a result of Newton’s Third Law

Consider a vase of flowers on a table; the Earth pulls the vase and the table pushes the vase. These two forces are equal and opposite. Therefore, as these two equal and opposite forces are acting on a single object in a state of rest, with no resultant force acting on it, this is a result of Newton’s First Law, not his Third.

From Newton’s Second Law, we know that the force acting on an object is equal to its rate of change of momentum; F = Δp / Δt

Rearranging this, we have: F Δt = Δp

The principle of conservation of momentum:

A rugby player of mass 75kg dives for the try line with a velocity of 8 ms-1. A defender of mass 120kg dives at him with a velocity of 6ms-1. Does the player score a try?

1. Draw a simple diagram, including masses and velocities. Add an arrow to show the ‘positive’ direction.

2. Calculate the total momentum before the collision

Total momentum before = [mass x velocity of player A] + [mass x velocity of player B]

= [75 x 8] + [120 x 6]

= 600 + [-720]

= -120 kgms-1

3. Calculate the total momentum after the collision

As momentum is conserved, momentum before = momentum after = -120 kgms-1

4. Work out the resulting velocity and answer the question

-120 kgms-1 / total mass of two players = -120kgms-1 /195 kg = -0.615 ms-1

As this is a negative answer, it is in the opposite direction to the ‘positive’ arrow on the diagram. A try therefore is not scored.

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A body remains at its state of rest or uniform motion unless an external force acts upon it.

Air Resistance

Friction

Motion

Momentum is the product of an object’s mass and velocity; mv. It is a vector quantity, the direction being the same as that of the velocity. Its units are kgms-1 or Ns.

The net force acting on a body is equal to its rate of change of momentum.

If body A exerts a force on body B then body B exerts a force equal in magnitude and opposite in direction on body A.

The impulse of a force is the product of the force and the time for which it acts, F$%79:;YZ[\ËÌÍ} ˜ 3BCðáÕðɽ­Ÿ“~“p“`J`J`=hÝfƒ6?CJOJQJaJ+h#\Ÿh#\Ÿ5?6?B*CJOJQJaJphÿh#\Ÿh#\Ÿ6?CJOJQJaJjh#\ŸU[pic]mHnHu[pic](jhÝfƒΔt. Its units or Ns (or kgms-1)

The impulse of a force is equal to the momentum change caused. The impulse is equal to the area beneath a force-time graph.

In any collision, the total momentum of the system before the collision is equal to the total momentum after the collision, provided that there is no external force acting.

75 kg

8ms-1

120 kg

6ms-1

Perfectly Elastic Collision

Momentum is conserved

Kinetic Energy is conserved

Total Energy is conserved

Inelastic Collision

Momentum is conserved

Kinetic Energy is NOT conserved

Total Energy is conserved

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