WORK AND ENERGY – Formula & Equation Sheet
Essential formulas and equations from Science, tailored for Class 9 in Science.
This one-pager compiles key formulas and equations from the WORK AND ENERGY chapter of Science. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
W = F × s
W is work (in joules), F is force (in newtons), and s is displacement (in meters). This formula defines work done on an object when a constant force is applied in the direction of the displacement.
E_k = (1/2) m v²
E_k is kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). This formula represents the energy possessed by an object due to its motion.
E_p = mgh
E_p is potential energy (in joules), m is mass (in kg), g is acceleration due to gravity (≈ 9.8 m/s²), and h is height (in meters). It defines gravitational potential energy acquired when an object is raised to a height.
P = W/t
P is power (in watts), W is work done (in joules), and t is time (in seconds). This formula measures the rate at which work is done or energy is transferred.
1 W = 1 J/s
This is the definition of a watt. It reflects that one watt is equivalent to one joule of work done per second.
E = E_k + E_p
E represents total mechanical energy, E_k is kinetic energy, and E_p is potential energy. This equation shows that total energy is the sum of kinetic and potential energies in a system.
F = ma
F is force (in newtons), m is mass (in kg), and a is acceleration (in m/s²). This formula relates the force acting on an object to its mass and the acceleration produced.
v² = u² + 2as
Here, v is final velocity, u is initial velocity, a is acceleration, and s is displacement. This equation of motion allows calculation of one variable when the others are known.
E_k (final) - E_k (initial) = Work done
This relation illustrates that the work done on an object results in a change in its kinetic energy. It is pivotal in analyzing energy transformations.
1 kJ = 1000 J
This conversion is useful when dealing with larger energy values. It highlights the relationship between joules and kilojoules.
Equations
W_total = W_positive + W_negative
This equation states that the total work done can be a combination of positive and negative work, reflecting the direction of the force relative to displacement.
F_net = m (v_f - v_i) / t
Here, F_net is the net force (in newtons), m is mass (in kg), v_f is final velocity, v_i is initial velocity, and t is time taken to achieve that change in velocity.
E_p (initial) + E_k (initial) = E_p (final) + E_k (final)
This conservation principle indicates that the total mechanical energy remains constant within an isolated system when only conservative forces act.
a = (v_f - v_i) / t
a represents acceleration (in m/s²), v_f is final velocity, v_i is initial velocity, and t is time taken. This formula is essential for understanding motion.
W = F × d × cos(θ)
Where θ is the angle between the force vector and displacement vector. This formula calculates work done when the force is applied at an angle.
P_avg = ΔE / Δt
P_avg represents average power. This is the average rate of energy change over the time interval Δt. Useful for calculating overall performance.
E_k = 1/2 mv^2
This redundant notation reaffirms the formula for kinetic energy empowering students to identify energy transformations.
E_p = mgh
This re-emphasizes potential energy derived from raising an object to a height, helping to reinforce critical energy principles.
θ = tan^-1 (y/x)
This trigonometric formula applies to the scenarios when analyzing motion at angles incorporating horizontal and vertical components.
Time = Distance / Speed
This foundational equation assists in calculating the time required to travel a distance at a constant speed and relates it directly to work and energy.
