Fundamental Laws of Physics: Motion, Energy, and Electricity
Newton’s Laws of Motion
Newton’s First Law of Motion
An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it.
Newton’s Second Law of Motion
The rate of change of momentum is proportional to the applied force, and the change of momentum occurs in the direction of the force.
Newton’s Third Law of Motion
Every action force has an equal and opposite reaction force which acts simultaneously.
Work
Work done by a force acting on a body is the product of the magnitude of the force and the displacement of the body in the direction of the force. When the force (F) acting on the body and the displacement (s) of the body have the same direction, the work done by the force is W = Fs.
If θ is the angle between the force F and displacement s, the work done by the force is W = Fs cos θ.
- If θ = 0°, cos θ = 1, W = Fs
- If θ = 90°, cos θ = 0, W = 0
- If θ = 180°, cos θ = -1, W = –Fs
Work has magnitude but not direction. Thus, it is a scalar quantity. The SI unit of work is the joule (J), and the CGS unit is the erg.
1 joule = 1 newton × 1 meter
1 J = 1 N.m
1 erg = 1 dyne × 1 centimeter = 1 dyne centimeter
1 J = 107 ergs
Energy
The capacity of a body to perform work is called its energy. It is a scalar quantity. Its units are the same as the units of work, i.e., the joule (SI unit) and the erg (CGS unit).
Positive, Negative, and Zero Work
- When the force and the displacement are in the same direction (θ = 0°), the work done by the force is positive.
- When the force and the displacement are in opposite directions (θ = 180°), the work done by the force is negative.
- When the applied force does not cause any displacement or when the force and the displacement are perpendicular to each other (θ = 90°), the work done by the force is zero.
Kinetic Energy
The energy which an object has because of its motion is called its kinetic energy. The kinetic energy of a body of mass m moving with velocity v is ½ mv2.
Law of Conservation of Energy
Energy can neither be created nor destroyed. It can be converted from one form into another. Thus, the total amount of energy in the universe always remains constant.
Power
Power is the time rate at which work is done. If W is the work done in time t, power (P) is given by P = W/t. It is a scalar quantity. The SI unit of power is the watt (W), and the CGS unit is the erg per second.
1 watt = 1 joule per second = 107 ergs per second
(1 joule = 107 ergs)
Power is also measured in units of horsepower (used in industry).
1 horsepower (hp) = 746 watts
The kilowatt-hour is a unit of energy used for commercial purposes.
1 kilowatt-hour (kWh) = 3.6 × 106 J
Ohm’s Law
The relationship between the current flowing through a wire (I) and the potential difference across its ends (V) can be obtained from the law that was given by the German scientist George Simon Ohm.
If the physical state of a conductor remains constant, the current (I) flowing through it is directly proportional to the potential difference (V) between its two ends.
I ∝ V
I = kV (k = constant of proportionality)
I × 1/k = V, 1/k = R = Resistance of the conductor
I × R = V, Hence V = IR or R = V/I
This is known as Ohm’s law.
We can obtain the SI unit of resistance from the above formula. Potential difference and current are measured in volts and amperes, respectively. The unit of resistance is called the ohm. It is indicated by the symbol Ω.
Example Problem: Resistance Calculation
The resistance of a 1m long nichrome wire is 6Ω. If we reduce the length of the wire to 70 cm, what will its resistance be?
Solution:
Given: L1 = 1m, R1 = 6Ω, L2 = 70cm = 0.7m, R2 = ?
In the usual notation:
R = ρL/A
∴ R1 = ρL1/A and R2 = ρL2/A
∴ R2/R1 = L2/L1 = 0.7/1 = 0.7
∴ R2 = 0.7R1 = 0.7 × 6Ω = 4.2Ω
This is the required resistance.