This chapter explains the concepts of work, energy, and power, which are essential for understanding physical systems.
WORK, ENERGY AND POWER – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the WORK, ENERGY AND POWER chapter of Physics Part - I. 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 · d · cos(θ)
W is work (in joules), F is the applied force (in newtons), d is the displacement (in meters), and θ is the angle between the force and displacement vectors. This formula calculates work done by a constant force acting over a distance.
K = (1/2) mv²
K represents kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). This shows the energy due to motion of an object.
W = ΔK
This states that the work done (W) by the net force on an object is equal to the change in kinetic energy (ΔK) of the object.
V(h) = mgh
V(h) denotes gravitational potential energy (in joules) at height h (in meters), m is mass (in kg), and g is the acceleration due to gravity (≈9.81 m/s²). This shows the energy stored due to an object's height.
P = W / t
P represents power (in watts), W is work done (in joules), and t is the time (in seconds) over which the work is done. It indicates the rate at which work is performed.
K = (1/2) kx²
K is the elastic potential energy (in joules) stored in a spring, k is the spring constant (N/m), and x is the displacement from equilibrium (in meters). This signifies the energy stored in a spring when compressed or stretched.
W = ∫F(x) dx
This represents the work done by a variable force F(x) as it moves from position xi to xf, calculated as an integral of the force over the displacement.
ΔK + ΔV = 0
This expresses the principle of conservation of mechanical energy, stating that the sum of the changes in kinetic energy (ΔK) and potential energy (ΔV) is zero when only conservative forces act.
v² = u² + 2as
This equation connects initial velocity (u), final velocity (v), acceleration (a), and displacement (s). It relates kinematic quantities for an object undergoing constant acceleration.
F = ma
This is Newton's second law, where F is the net force (in newtons), m is mass (in kg), and a is acceleration (in m/s²). It describes the relationship between force, mass, and acceleration.
Equations
W_total = W_g + W_r
This equation relates the total work (W_total) done on a system to the work done by gravitational force (W_g) and the work done by resistive forces (W_r).
K_final - K_initial = W_net
This equation illustrates that the change in kinetic energy is equal to the work done by the net force acting on the object.
V = K + U
This states that the total mechanical energy (V) is the sum of the kinetic energy (K) and potential energy (U) of an object.
P_avg = ΔE / Δt
This defines average power (P_avg) as the change in energy (ΔE) divided by the time interval (Δt) over which the change occurs.
F_s = -kx
This is Hooke's law, stating that the spring force (F_s) acts in the opposite direction of the displacement (x) and is proportional to the displacement amount, where k is the spring constant.
F_net = ma
This equation states that the net force (F_net) acting on an object is equal to the product of its mass (m) and acceleration (a).
mgh = (1/2) mv² + (1/2) kx²
This equation represents energy conservation, expressing that gravitational potential energy (mgh) converts to kinetic energy and elastic potential energy when falling.
W = ∫F·dx
This describes the work done by a force (F) along a path (dx) as an integral, useful for non-constant forces.
F · d = W
This signifies that the work done by a force (F) on an object while it displaces through a distance (d) is equal to the dot product of the force and displacement vectors.
K = W
Indicates that the work done on an object is equal to its kinetic energy, illustrating the work-energy principle.
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