Dynamics Flashcards
Define force.
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
Determine the SI base unit of momentum.
p= F x t
= ma x t
= kg m/s ^ 2 x s
= kg m/s
Define momentum.
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
Define linear momentum.
Linear momentum is defined as the product of mass and linear velocity (in a straight line)
Define mass
Mass is a property of a body that resists change in motion [measure of a body‘s inertia].
Derive the formula:
F=ma
F= delta p/t
F=mv-mu/t
F=m(v-u)/t. a=v-u/t
So, F= ma
Define inertia.
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)
In what direction does the acceleration or deceleration of a body occur?
The acceleration/deceleration occur in the direction of the resultant force.
What are the units of momentum?
Ns
Kg m/s
Use the chain rule to obtain a formula involving m and b from the formula:
F=dp/dt. When is this formula used?
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
What does newtons first law of motion state?
A body will remain at rest open today its motion with constant velocity in a straight line unless acted upon by a RESULTANT force.
What are the conditions for equilibrium?
- the resultant force in any direction is 0 N
2. The resultant torque about any point is 0 Nm
What does newton second law state?
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
What is the first case of newtons second law?
- 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
When can the first case of newtons second law be applied?
Only when the mass is constant.
Define 1 N and use this to prove that
F=ma
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
What is the second case of newton second law?
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
What is the third case of newtons second law?
When BOTH MASS AND VELOCITY are not constant
F=dp/dt = d(mv)/dt
F= m.dv/dt + v.dm/dt
Define impulse and derive a formula for impulsive force.
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
What is the formula for impulse?
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)
What does the gradient of a momentum time graph give?
F= dp/ dt
Therefore the gradient give the resultant impulsive force
What does the area under a force time graph give?
The impulse/ change in momentum
I.e F =dp/dt
dp= Ft
What does newtons third law state?
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.
Define weight.
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
What are the conditions for two forces to be an action reaction pair?
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
Describe air resistance/drag force
It is a force that resists motion [It actsin the opposite direction to the motion]
Drag force is DIRECTLY PROPORTIONAL to:
- VELOCITY
- CROSS SECTIONAL AREA
(Study terminal velocity and acceleration graphs) ms Lee and seebaluck
What does the principle of conservation of momentum state?
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
Check derivation of newtons theirs lae and conservation of momentum relationship( ms lee )
..
What are the properties of an elastic collision?
- Momentum is conserved
- Kinetic energy is conserved
Sum of initial kinetic energy =sum of final kinetic energy. - For a perfectly elastic collision:
Relative velocity of approach = to relative velocity of separation
State the relative velocity equation
U1 - U2 = V2 - V1
Or
U1- U2 = - (V1-V2)
Taking movement to the right as positive
(Check derivation miss Lee notes)
What are the properties of an inelastic collision?
- Momentum is conserved
- 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)
In what forms is kinetic energy lost during an inelastic collision
Kinetic energy is lost in the form of heat, sound, or deformation.
Collisions in 2D
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
Notes
- During a head on elastic collision between IDENTICAL bodies there is an exchange of velocity
- Check questions
What is the relationship between kinetic energy and momentum
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
