Two particles of equal mass move at the same speed in opposite directions. How do their momenta compare?

They have the same magnitude of momentum but opposite signs . Momentum is a vector whose direction is the direction of motion, so a particle with a negative velocity has a negative momentum.

A braking force acts on a car that is moving to the right. In which direction does the impulse of that force act?

To the left , opposite to the car's motion. The impulse of a force always acts in the same direction as the force , and a braking force acts against the motion.

A racket hits a tennis ball. What does Newton's third law tell you about the impulses involved?

The racket exerts an impulse on the ball and the ball exerts one back on the racket, and the two are equal in magnitude and opposite in direction . That is why the ball is propelled forwards while the racket is slowed down.

Define a direct collision .

A direct collision is a collision between two objects that are travelling along the same straight line . Before it they may be moving in the same direction, in opposite directions, or one of them may be stationary.

What does it mean for two objects to coalesce , and what may you then do?

To coalesce is to merge into a single object, which then moves off as one. Afterwards you may treat them as one particle whose mass is the sum of the two masses, or equally as two particles moving with the same velocity.

How is an explosion like a direct collision?

An explosion is one object separating into two that travel along the same straight line, so the same momentum equation applies to it. A bullet fired from a gun is the standard example: the object may start at rest, and the two parts then move off in opposite directions.

True or False? Two objects moving towards each other along the same line must both change direction when they collide.

False. At least one of them must, because two objects cannot pass through each other, so they cannot both carry on exactly as they were. The other may simply continue in the same direction, more slowly than before.

What must be true of the forces acting for momentum to be conserved?

There must be no external forces acting on the two objects. That is why these problems are set on a smooth horizontal surface: friction would be an external force, and it would change the total momentum.

You do not know which way a particle moves after a collision. What do you do, and how do you read the answer?

Choose a direction for it anyway, and write its velocity into the equation with the sign that choice gives it. If the velocity comes out negative , the particle is really moving the opposite way to the one you assumed.

International A Level (IAL)MathsEdexcelMechanics 1FlashcardsDynamics & Statics of a ParticleMomentum, Impulse & Collisions

Momentum, Impulse & Collisions (Edexcel International A Level (IAL) Maths: Mechanics 1): Flashcards

Exam code: YMA01

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Fill in the blanks to complete the momentum of a particle:
$momentum =______\times______$

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Cards in this collection (17)

Fill in the blanks to complete the momentum of a particle:
$momentum =______\times______$
The completed definition is:
$momentum = mass \times velocity = m v$
Any object that has mass and is moving has momentum, and $m v$ measures the quantity of motion it has.
Define the impulse of a constant force.
The impulse of a constant force $F$ N acting for $t$ seconds is the product of the two, $I = F t$ .
It is a vector quantity, and it is measured in newton seconds (N s).
Two particles of equal mass move at the same speed in opposite directions. How do their momenta compare?
They have the same magnitude of momentum but opposite signs.
Momentum is a vector whose direction is the direction of motion, so a particle with a negative velocity has a negative momentum.
A braking force acts on a car that is moving to the right. In which direction does the impulse of that force act?
To the left, opposite to the car's motion.
The impulse of a force always acts in the same direction as the force, and a braking force acts against the motion.
True or False?
Impulse and momentum are measured in the same unit.
True.
Impulse is measured in newton seconds and momentum in ${kg m s}^{- 1}$ , and those are the same unit.
A newton is a ${kg m s}^{- 2}$ , so multiplying it by seconds gives ${kg m s}^{- 1}$ .
Define the impulse-momentum principle.
The impulse-momentum principle states that the impulse of a force equals the change in momentum it produces:
$I = m v - m u$
Here $m$ is the mass, $u$ the initial velocity and $v$ the final velocity.
A dog of mass 15 kg runs at $6 {m s}^{- 1}$ . Find its momentum.
Multiply the mass by the velocity:
$15 \times 6 = 90 {kg m s}^{- 1}$
The answer carries a direction as well as a size, so it is 90 in the direction the dog is running.
A car of mass 1200 kg moving at $16 {m s}^{- 1}$ is braked by a constant force of 1800 N for 5 seconds. Find its new speed.
The impulse is $1800 \times 5 = 9000 N s$ acting against the motion, so taking the direction of travel as positive it enters as $- 9000$ :
$1200 v - 1200 \times 16 = - 9000$
That gives $1200 v = 10200$ , so the new speed is $8.5 {m s}^{- 1}$ .
A racket hits a tennis ball. What does Newton's third law tell you about the impulses involved?
The racket exerts an impulse on the ball and the ball exerts one back on the racket, and the two are equal in magnitude and opposite in direction.
That is why the ball is propelled forwards while the racket is slowed down.
Define a direct collision.
A direct collision is a collision between two objects that are travelling along the same straight line.
Before it they may be moving in the same direction, in opposite directions, or one of them may be stationary.
What does it mean for two objects to coalesce, and what may you then do?
To coalesce is to merge into a single object, which then moves off as one.
Afterwards you may treat them as one particle whose mass is the sum of the two masses, or equally as two particles moving with the same velocity.
Two particles of masses $m_{1}$ and $m_{2}$ have velocities $u_{1}$ and $u_{2}$ before a direct collision and $v_{1}$ and $v_{2}$ after it. Fill in the blanks to complete the conservation of momentum:
$m_{1} u_{1} + m_{2} u_{2} =______+______$
The completed equation is:
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
In words, the total momentum after the collision is the same as the total momentum before it.
How is an explosion like a direct collision?
An explosion is one object separating into two that travel along the same straight line, so the same momentum equation applies to it.
A bullet fired from a gun is the standard example: the object may start at rest, and the two parts then move off in opposite directions.
True or False?
Two objects moving towards each other along the same line must both change direction when they collide.
False.
At least one of them must, because two objects cannot pass through each other, so they cannot both carry on exactly as they were.
The other may simply continue in the same direction, more slowly than before.
What must be true of the forces acting for momentum to be conserved?
There must be no external forces acting on the two objects.
That is why these problems are set on a smooth horizontal surface: friction would be an external force, and it would change the total momentum.
You do not know which way a particle moves after a collision. What do you do, and how do you read the answer?
Choose a direction for it anyway, and write its velocity into the equation with the sign that choice gives it.
If the velocity comes out negative, the particle is really moving the opposite way to the one you assumed.
Particles $P$ (3 kg) and $Q$ (5 kg) travel towards each other at $4 {m s}^{- 1}$ and $2 {m s}^{- 1}$ and collide, after which $P$ moves back the way it came at $1 {m s}^{- 1}$ . Find the speed of $Q$ .
Take $P$ 's original direction as positive, so $Q$ starts at $- 2$ and $P$ finishes at $- 1$ :
$3 (4) + 5 (- 2) = 3 (- 1) + 5 v$
That gives $2 = 5 v - 3$ , so $v = 1 {m s}^{- 1}$ , and the positive sign shows that $Q$ has reversed direction too.

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