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Physics > Dynamics > Flashcards

Dynamics Flashcards

1
Q

Define force.

A

Force is defined as the rate of change of momentum with respect to time.

Force = change in momentum/ time
Force= delta p/t

Force: Newton, N
p : Newton second, Ns
t: second, s

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2
Q

Determine the SI base unit of momentum.

A

p= F x t
= ma x t
= kg m/s ^ 2 x s
= kg m/s

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3
Q

Define momentum.

A

Momentum is defined as the product of mass and velocity.

•Momentum is a vector quantity And is in the same direction as the velocity.

Momentum= mass x velocity 
p= mv
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4
Q

Define linear momentum.

A

Linear momentum is defined as the product of mass and linear velocity (in a straight line)

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5
Q

Define mass

A

Mass is a property of a body that resists change in motion [measure of a body‘s inertia].

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6
Q

Derive the formula:

F=ma

A

F= delta p/t
F=mv-mu/t
F=m(v-u)/t. a=v-u/t
So, F= ma

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7
Q

Define inertia.

A

Inertia is defined as the tendency of a substance to maintain its state of rest(velocity=0) or uniform motion in a straight line(velocity constant)

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8
Q

In what direction does the acceleration or deceleration of a body occur?

A

The acceleration/deceleration occur in the direction of the resultant force.

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9
Q

What are the units of momentum?

A

Ns

Kg m/s

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10
Q

Use the chain rule to obtain a formula involving m and b from the formula:
F=dp/dt. When is this formula used?

A

F=dp/dt
F=d(mv)/dt. Since p=mv

Therefore,

F= m.dv/dt + v.dm/dt

For constant velocity,
F= v.dm/dt. As m.dv/dt= 0

For constant mass,
F=m.dv/dt. As v.dm/dt = 0

This formula is applied when both velocity and mass can vary.

Note: dv/dt = change in velocity

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11
Q

What does newtons first law of motion state?

A

A body will remain at rest open today its motion with constant velocity in a straight line unless acted upon by a RESULTANT force.

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12
Q

What are the conditions for equilibrium?

A
  1. the resultant force in any direction is 0 N

2. The resultant torque about any point is 0 Nm

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13
Q

What does newton second law state?

A

The resultant force acting on a body is directly proportional to the rate of change of momentum and is in the direction of the change in momentum.

F= k. dp/dt

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14
Q

What is the first case of newtons second law?

A
  1. MASS CONSTANT(derivation of F=ma)
F= k. dp/dt
F= k. d(mv)/dt.  Mass is constant
Therefore, 
F= k.m(dv/dt).   dv/dt=a
F= K. ma
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15
Q

When can the first case of newtons second law be applied?

A

Only when the mass is constant.

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16
Q

Define 1 N and use this to prove that

F=ma

A

1 N is defined as the RESULTANT FORCE required to give a mass of 1 kg an acceleration of 1 m/s squared

F=K.ma
F= 1 N. m=1kg. a= 1 m/s ^2
Therefore, k=constant= 1

So, F(RESULTANT) =ma

17
Q

What is the second case of newton second law?

A

Where VELOCITY is constant:

In this case,
F = dp/dt
F= d(mv)/dt
F=m.dv/dt + v.dm/dt. Velocity is constant (dv/dt = 0)

Therefore,
F = v. dm/dt

Note: dm/dt = mass flow rate

18
Q

What is the third case of newtons second law?

A

When BOTH MASS AND VELOCITY are not constant

F=dp/dt = d(mv)/dt

F= m.dv/dt + v.dm/dt

19
Q

Define impulse and derive a formula for impulsive force.

A

Impulse is defined as the change in momentum, delta p. Or the product of force and the time for which the force acts.
Unit: Ns

F= dp/dt = delta mv/ delta t
Therefore,
F (IMPULSIVE FORCE) =final momentum - initial momentum / t

When mass is constant,
F = mv-mu / t

20
Q

What is the formula for impulse?

A

Impulse = change in momentum

Delta p = delta mv

From : F= delta p / t
We get: F = delta mv / t

Therefore : delta mv = Ft.

Therefore
impulse= change In momentum = delta mv = Ft

This is why the unit of momentum is NS

Note: F is the impulsive force ( resultant force that produces a change in momentum)

21
Q

What does the gradient of a momentum time graph give?

A

F= dp/ dt

Therefore the gradient give the resultant impulsive force

22
Q

What does the area under a force time graph give?

A

The impulse/ change in momentum

I.e F =dp/dt
dp= Ft

23
Q

What does newtons third law state?

A

If a body A exerts a force on body B then body B will exerts a force on body A of the SAME MAGNITUDE , SAME KIND but in OPPOSITE DIRECTION.

24
Q

Define weight.

A

Weight is the pull of gravity acting on your body is defined as a product of its mass and acceleration of free fall.

W= mg

25
Q

What are the conditions for two forces to be an action reaction pair?

A

Number one: the forces should be of the same kind.
Number two: the forces need to be of the same magnitude.
Number three: the forces need to be acting on mutually opposite bodies( DIFFERENT BODIES)
Number four: the forces need to be opposite in direction

26
Q

Describe air resistance/drag force

A

It is a force that resists motion [It actsin the opposite direction to the motion]

Drag force is DIRECTLY PROPORTIONAL to:

  1. VELOCITY
  2. CROSS SECTIONAL AREA

(Study terminal velocity and acceleration graphs) ms Lee and seebaluck

27
Q

What does the principle of conservation of momentum state?

A

The total momentum of a system of interacting bodies remains constant [is conserved] provided that no external force acts on the system.

SUM OF MOMENTA BEFORE= SUM OF MOMENTA AFTER

I.e m1u1 + m2u2 = m1v1 + m2 v2

It also states that for a system of interacting bodies the vector sum of the change in momenta is zero provided no external force acts

Check proof ( ms Lee notes)
I.e delta p1 = delta p2
Therefore
P1-p2= 0
28
Q

Check derivation of newtons theirs lae and conservation of momentum relationship( ms lee )

A

..

29
Q

What are the properties of an elastic collision?

A
  1. Momentum is conserved
  2. Kinetic energy is conserved
    Sum of initial kinetic energy =sum of final kinetic energy.
  3. For a perfectly elastic collision:

Relative velocity of approach = to relative velocity of separation

30
Q

State the relative velocity equation

A

U1 - U2 = V2 - V1

Or

U1- U2 = - (V1-V2)

Taking movement to the right as positive

(Check derivation miss Lee notes)

31
Q

What are the properties of an inelastic collision?

A
  1. Momentum is conserved
  2. Kinetic energy is not conserved [Kinetic energy is lost)
    Sum of kinetic energy before >sum of kinetic energy after.
    Kinetic energy lost= initial kinetic energy - final kinetic energy

Note: For a perfectly inelastic collision the bodies stick together after impact (coalesce)

32
Q

In what forms is kinetic energy lost during an inelastic collision

A

Kinetic energy is lost in the form of heat, sound, or deformation.

33
Q

Collisions in 2D

A

The total momentum in any direction must be conserved that is:

Sum of initial momenta X = sum of final momenta X

Sum of initial momenta Y = sum of final momenta Y

34
Q

Notes

A
  1. During a head on elastic collision between IDENTICAL bodies there is an exchange of velocity
  2. Check questions
35
Q

What is the relationship between kinetic energy and momentum

A

KINETIC ENERGY= p^2/ 2m

Proof:
p= mv. (Square both sides)

p^2 = m^2 x v^2. (Multiply by 1/2)

p^2/2 = m x (1/2 m.v^2)

Therefore,

Ek= p^2/2m

Physics (2 decks)

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