Dynamics Flashcards
(35 cards)
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
