Definitions [9]
Define 1 Dyne.
1 dyne is that force which when acting on a body of mass 1 gram, produces an acceleration of 1 cm s-2 in it.
1 dyne = 1 g × 1 cm s-2.
Force is defined as the rate of change of linear momentum of a body with respect to time.
Define an Inclined plane.
An inclined plane is usually a smooth, flat rigid surface inclined at an angle (θ) to the horizontal. It is used to raise heavy loads with a relatively small force. The longer the slope, the smaller is the effort needed.
Define contact forces.
The forces which are applied on a body through a connector, are called contact forces. Forces like Frictional force, Mechanical force, etc., are the forces of contact.
Answer the following.
Define weight.
The gravitational force acting on an object is called the weight of the object.
Define the term “weight of a body”
The weight of the body is the force with which the earth attracts it towards the centre. It depends on acceleration due to gravity.
A force is seen to act through direct contact of the objects or via one more object. Such a force is called 'Contact force.'
OR
The forces experienced by a body due to physical contact with another object, e.g., frictional force, normal force, are called contact forces.
A force is applied between two objects even if the two objects are not in contact; such a force is called a 'Non-contact force.'
OR
The forces experienced by a body without any physical contact with another object, e.g., gravitational force, electrostatic force, are called non-contact forces.
Define Newton’s second law of motion.
Newton’s second law of motion states that the rate of change of momentum is directly proportional to force applied and takes place in the direction of the force.
Formulae [4]
\[\overset{\rightarrow}{\operatorname*{F}}=\frac{d\overset{\rightarrow}{\operatorname*{p}}}{dt}=\frac{d(m\overset{\rightarrow}{\operatorname*{v}})}{dt}\]
or
\[\begin{array}
{rcl}\vec{F} & = & m\vec{a}
\end{array}\](if mass m is constant)
\[\vec F\] = m \[\frac{d\vec{\mathrm{v}}}{dt}\] = m\[\vec a\] ... (for constant mass)
Thus, if \[\vec F\] = 0, \[\vec v\] is constant. Hence, if there is no force, velocity will not change. This is nothing but Newton's first law of motion.
General Form: \[\vec F\] =\[\frac{d\vec{p}}{dt}\]
For Constant Mass: \[\vec F\] = m\[\vec a\]
Momentum: \[\vec p\] = m\[\vec v\]
\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]
Theorems and Laws [4]
Statement:
Every inanimate object continues to be in a state of rest or of uniform unaccelerated motion along a straight line, unless it is acted upon by an external, unbalanced force.
Importance:
- It shows the equivalence between the state of rest and the state of uniform motion along a straight line — the distinction lies only in the choice of frame of reference.
- It defines force as a physical entity that brings about a change in the state of motion or rest of an object.
- It defines inertia as a fundamental and inherent property of every physical body by virtue of which it resists any change in its state of rest or uniform motion along a straight line.
Statement:
The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.
F = Δp = m\[\frac {dv}{dt}\] = ma
Importance:
- It provides a mathematical formulation for the quantitative measure of force: F = \[\frac {Δp}{Δt}\] = ma.
- It defines momentum as the product of mass and velocity: p = mv.
- Aristotle's fallacy is overcome by establishing that it is the resultant unbalanced force — not force itself — that is required to maintain a change in the state of motion.
Statement:
To every action (force) there is always an equal and opposite reaction (force).
Importance:
- It defines action and reaction as a pair of equal and opposite forces acting along the same line — whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first.
- Action and reaction forces always act on different objects and therefore never cancel each other out.
Statement: The total momentum of a system of particles remains constant as long as no external forces act upon it.
-
When no external forces act on colliding objects, the vector sum of linear momentum of each body remains constant and is not affected by mutual interaction.
Key Points
- Force is a Vector Quantity
- Unit of Force is Newton (symbol N) or kilogram-force (symbol kgf), where 1 kgf = g N if g is the acceleration due to gravity at that place (= 9·8 m s-2 average value on the earth's surface).
- Newton's First Law states that a body at rest or in uniform motion stays that way unless an external unbalanced force acts on it.
- The law explains inertia, which is an object's resistance to changing its state of motion on its own.
- The 'state of rest' and 'state of uniform motion' are considered equivalent; both require a net unbalanced force to change.
- Force is defined by the law as the entity that changes a body’s state of motion.
- A balanced force results in a net force of zero, meaning no acceleration.
- An unbalanced force results in a net force that causes acceleration and changes the state of motion.
- Inertia is quantitatively measured by the object's mass (inertial mass).
Statement: The initial momentum of a rocket at its launching pad is zero. When fired, the exhaust gases rush downward at high speed. To conserve momentum, the rocket moves upwards.
Thrust on the rocket:
The negative sign indicates that the direction of thrust is opposite to the direction of escaping gases.
Acceleration of the rocket:
where v = velocity of exhaust gases and \[\frac {dm}{dt}\] = rate of fuel consumption = rate of ejection of fuel.
