Momentum | CAIE 9702 Paper 2 Notes · Conquer Your A Levels

Paper 2

Physics9702

Momentum

The rest of this chapter is about collisions. To predict a collision you need one new quantity.

A collision calculation needs a quantity that includes both mass and velocity. Multiply them and you get .

The definition

p = mv

Symbols

$p$ = linear momentum (kg m s⁻¹)
$m$ = mass (kg)
$v$ = velocity (m s⁻¹)

Linear momentum is the product of mass and velocity. That sentence, word for word, is a one-mark definition.
The unit kg m s⁻¹ has no special name. N s is an equivalent unit (lesson 3.12 shows why).
Momentum is a vector. Its direction is the direction of the velocity. In one dimension, choose a positive direction and give the opposite way a minus sign.

Definition

1 mark

What is meant by linear momentum?

Model answer: The product of mass and velocity.

A large lorry moving slowly and a much smaller car moving quickly, both to the right. — A large mass at low speed can have the same momentum as a small mass at high speed. Mass or speed alone is not enough.

Worked example

Smallest case: one moving ball

A ball of mass 3.0 kg rolls at 4.0 m s⁻¹. Find its momentum.

$p = mv = 3.0 \times 4.0 = 12 \text{ kg m s}^{-1}$ in the direction of motion.

Answer

p = 12 \text{ kg m s}^{-1}

Very different objects can have the same momentum. A 12 000 kg lorry rolling at 5.0 m s⁻¹ and a 1500 kg car driving at 40 m s⁻¹ both have p = 60 000 kg m s⁻¹.

Your turnExam-style

A 0.25 kg ball moves to the left at 8.0 m s⁻¹. Taking right as positive, calculate its momentum.

Show worked answer

Left means $v=-8.0\ \text{m s}^{-1}$ , so $p=0.25\times(-8.0)=-2.0\ \text{kg m s}^{-1}$ .

Answer

p=-2.0\ \text{kg m s}^{-1}

Momentum is not kinetic energy

Both are built from $m$ and $v$ , but they behave differently.
Momentum $p = mv$ is a vector: two equal objects moving opposite ways have total momentum zero.
Kinetic energy $E_k = \tfrac{1}{2}mv^2$ is a scalar: the same two objects have twice the kinetic energy of one, never zero.

Opposite momenta can cancel because momentum is a vector. Kinetic energies cannot cancel because kinetic energy is a scalar.

Momentum

The rest of this chapter is about collisions. To predict a collision you need one new quantity.

A collision calculation needs a quantity that includes both mass and velocity. Multiply them and you get .

The definition

p = mv

Symbols

$p$ = linear momentum (kg m s⁻¹)
$m$ = mass (kg)
$v$ = velocity (m s⁻¹)

Linear momentum is the product of mass and velocity. That sentence, word for word, is a one-mark definition.
The unit kg m s⁻¹ has no special name. N s is an equivalent unit (lesson 3.12 shows why).
Momentum is a vector. Its direction is the direction of the velocity. In one dimension, choose a positive direction and give the opposite way a minus sign.

Definition

1 mark

What is meant by linear momentum?

Model answer: The product of mass and velocity.

Worked example

Smallest case: one moving ball

A ball of mass 3.0 kg rolls at 4.0 m s⁻¹. Find its momentum.

$p = mv = 3.0 \times 4.0 = 12 \text{ kg m s}^{-1}$ in the direction of motion.

Answer

p = 12 \text{ kg m s}^{-1}

Very different objects can have the same momentum. A 12 000 kg lorry rolling at 5.0 m s⁻¹ and a 1500 kg car driving at 40 m s⁻¹ both have p = 60 000 kg m s⁻¹.

Your turnExam-style

A 0.25 kg ball moves to the left at 8.0 m s⁻¹. Taking right as positive, calculate its momentum.

Show worked answer

Left means $v=-8.0\ \text{m s}^{-1}$ , so $p=0.25\times(-8.0)=-2.0\ \text{kg m s}^{-1}$ .

Answer

p=-2.0\ \text{kg m s}^{-1}

Momentum is not kinetic energy

Both are built from $m$ and $v$ , but they behave differently.
Momentum $p = mv$ is a vector: two equal objects moving opposite ways have total momentum zero.
Kinetic energy $E_k = \tfrac{1}{2}mv^2$ is a scalar: the same two objects have twice the kinetic energy of one, never zero.

Opposite momenta can cancel because momentum is a vector. Kinetic energies cannot cancel because kinetic energy is a scalar.