Question 1

What is the work-energy theorem?

Accepted Answer

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE = ½mv₂² - ½mv₁². Work is defined as the dot product of force and displacement: W = F⃗·d⃗ = Fd cosθ, where θ is the angle between the force vector and the displacement vector.

Question 2

How do you calculate work done by a spring?

Accepted Answer

For a spring with spring constant k compressed or stretched by displacement x from its natural length, the work done is W = ½kx². This equals the triangular area under the F-x graph (F = kx). For displacement from x₁ to x₂ the work is W = ½k(x₂² - x₁²). The negative of this is the elastic potential energy stored: U = ½kx².

Question 3

How is mechanical power calculated?

Accepted Answer

Mechanical power P (watts) is the rate of work done: P = dW/dt. When force F and velocity v are known, P = F⃗·v⃗ = Fv cosθ. For a rotating shaft, P = Tω where T is torque and ω is angular velocity. To convert horsepower: 1 hp = 745.7 W. For constant force over distance x in time t: P = W/t = Fx/t.

Question 4

How is the work-energy theorem used in CAE?

Accepted Answer

Key CAE applications: (1) Energy balance verification in crash/impact simulations (LS-DYNA): internal energy + kinetic energy = external work; (2) Principle of virtual work in FEM — elastic strain energy equals work of external forces at equilibrium; (3) Motor and drive train power-torque calculations (P = Tω); (4) Estimating impact velocity in drop tests: mgh = ½mv² gives v = √(2gh).

Work-Energy Theorem & Power Calculator

F–x chart (area = work)

Kinetic energy KE vs displacement

Theory