Ch#3 : Dynamics Flashcards
Learn about motion and its causes.
State and explain Force? , Define Dynamics
Dynamics : The study of motion of objects and its cause.
Definition : A force moves or tends to move , stops or tends to stop the motion of a body.A force can also change the direction of motion of a body.
Vector Quantity , SI Unit : N or kgm/s²
Define and explain inertia and momentum
Inertia : The property of a body which due to which it resists a change in its stae of rest or motion.
Galileo first observed this phenomenon.
Newton related it to the mass of the body. The greater the mass , the greater the inertia.
Momentum : of a body is the quantity of motion it possesses due to its mass and velocity.
P = mv
Vector Quantity , SI Unit : kgm/s¹
What is a net force , explain Newton’s 1st law of motion.
Net force : Is the resultant of all forces acting on the body.
Definition : A body continues in its state of rest or of uniform motion in a straight line provided no net force acts on it.
Since it deals with the inertial property of matter , it is also called the law of inertia.
Example : Passengers standing in a bus fall forward when brakes are applied. Ths is because the upper parts of thier bodies continue thier motion while the lower parts in contact with bus stop moving.
State and explain Newton’s 2nd law of motion. What is a newton and prove 1Ns = 1kgm/s¹
Definition : When a net force acts on a body , it produces acceleration in thw body in the direction of the net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to the mass.
a ∝ F
a ∝ 1/m
a ∝ F/m
F ∝ ma
Putting k as proportional constant ,
F = kma
In SI units , the value of k comes out to be 1 ,
F = ma
Si Unit of force is Newton(N)
Newton : 1Newton is the force that produces an acceleration of 1m/s² in a body of mass 1 kg.
1N = 1kgm/s²
Prove : 1Ns = kgm/s¹
kgm/s² X s = kgm/s¹
kgm/s¹ = kgm/s¹
Differ between mass and weight.
Mass : the mass of a body is the quantity of matter possessed by a body.
It is a scalar quantity and does not change with the change of place. It is measured by comparison with the standard masses on a beam balance.
SI Unit : kg(base quantity)
Weight : Weight of a body is the force of gravity acting on it.
It depends on the value of g ,
w = mg
Weight is a force and it is a Vector Quantity. Si Unit : Newton(derived quantity)
It is measured by a spring balance.
State and explain Newton’s 3rd with 2 examples.
Definition : To every action there is an equal and opposite reaction
Explanation : Let body A exert a force on body B , body B reacts and exerts a force on A. The force exerted by A on B is the action force and the force exerted by B on A is the reaction force.
According to this law , action is always accompanied by a reaction force and the two forces are equal and opposite of each other.Note that the action and reaction forces act on different bodies
Example : Consider a book lying on a table. The weight of the book is acting on the table in the downward direction.This is the action. The reaction of the table acts upwards on the book.
A rocket works on the same principle. When its fuel burns , hot gases escape out of its tail with a very high speed.The reaction of these gases causes the Rocket to move opposite to the gases rushing out of its tail.
What is the relationship between force and momentum?
Definition : When a net force acts on a body , it produces acceleration in the body and will be equal to the rate of change of momentum of the body.
SI Unit : Ns/kgm/s¹
Explanation : consider a body of mass m moving with initial velocity Vi. Let a force F act on a body producing acceleration in it. Latest scanners lost day after time t become Vf.If Pi and Pf are the initial and final momentum respectively ,
Pi = mVi Pf = mVf
Pf - Pi = m(Vf - Vi)
Rate of change of momentum ,
Pf - Pi/t = m(Vf - Vi)/t
Vf - Vi/t = a
Pf - Pi/t = ma
According to Newton’s 2nd law ,
F = ma
So , Pf - Pi/t = F
State and explain the law of conservation of momentum.
System : A group of bodies within certain boundaries.
Isolated system : A group of interacting bodies on which no external force is acting.
Law of Conservation of momentum : The momentum of an isolated system of two or more interacting bodies remains constant.
Diagram : Spheres
Explanation: consider an isolated system of two spheres of mass m1 and m2. They are moving in a straight line with initial velocities u1 and u2.u1 > u2.The sphere of mass m1 approaches the sphere of mass m2 as they move.
Pi of m1 = m1u
Pi of m2 = m2u2
Total Pi of the system before collision = m1u1 + m2u2
After some time , mass m1 hits m2 with some force. According to Newton’s 3rd law , m2 exerts an equal but opposite reaction force on m1 and the velocites become v1 and v2 respectively after collision.
Pf of m1 = m1v1
Pf of m2 = m2v1
Total final momentum = m1v1 + m2v2
According to law of conversation of momentum ,
Total initial momentum = Total final momentum
m1u1 + m2u2 = m1v1 + m2v2
Explain the law of conservation of momentum of momentum with the help of a system if gun and bullet.
Consider a system of a gun and bullet. Before firing the gun both the gun and the bullet are at rest , so the total momentum is ZERO. As it is fired , a bullet shoots out of the gun and acquires momentum. To conserve the momentum of the system , the gun recoils.According to the law of conservation of momentum , the total momentum of the gun and bullet will be zero after the gun is fired.Let m be the mass of the bullet and v be its velocity. Let M be the mass of the gun and V be its velocity with which it recoils.
Total momentum of the gun and bullet after it is fired = MV + mv
According to law of conservation of momentum ,
Total momentum of the gun and bullet after firing = Total momentum of the gun and bullet before firing
MV + mv = 0
MV = -mv
V = -mv/M
Negative sign indicates that the velocity of the gun is opposite to the bullet. Since the mass of the gun is larger , the recoil velocity is smaller than the velocity of the bullet.
State and explain centripetal force and cetrifugal force.
Definition : Centripetal force is a force that keeps a body moving in a circle.
Explanation : Let a body of mass m move with uniform velocity V in a circle of radius r.The acceleration ac is produced by centripetal force Fc , given by
ac = v²/r
According to Newton’s 2nd law ,
Fc = m ac
Fc = mv²/r
Centrifugal force : is the centripetal reaction which pulls the string outwards.
Why is rolling friction smaller than sliding friction?
When a wheel is rolled over the ground , the friction between the wheel and ground at the point of contact provides the reaction force. The reaction force acts at the contact points in a direction opposite to the applied force.The wheel rolls without rupturing the cold welds so rolling friction is much smaller than sliding friction.
4 methods of reducing friction?
- Making the skiding surfaces smooth.
- Making fast moving objects have a streamlined (fish shaped) shape.This causes the smooth flow of air reducing air resistance.
- Lubricating the sliding surfaces
- Using ball bearings as rolling friction is less than sliding friction.
