WPE Flashcards
Work
Work is said to be done whenever a force acts on a body and the body moes through some distance in the direction of the force
Work done formula
W = F . s = Fs cos theta
Work done by variable force
W = integral (F(x) dx)
Work done by kinetic energy and potential energy
KE = 1/2 mv^2
PE = mgh
Derive KE using calculus method
dW = F . ds = Fds
F = ma = m (dv / dt)
dW = m(dv/dt) * ds = mv dv
W = integral dW = 1/2 * mv^2
Prove conservation of mechanical energy in a freely falling body
Highest point = mgh
Mid point = mg(h-x) + 1/2m(2gx) = mgh
Lowest point = 1/2m * 2gh = mgh
Potential energy of a spring derivation
dW = dx = -kxdx
W = integral (dW) = -k [x^2/2]f to initial
W = 1/2kxi^2 - 1/2kxf^2
All formulas related to springs
F = -kx
k = F / x
W = 1/2 kx^2
Power formula
Power is the rate of doing work
P = F * v
Elastic Collision
- Momentum is conserved
- KE is conserved
- Coeff of restitution is 1
Inelastic collisions
- Momentum is conserved
- KE is not conserved
- Coeff of restitution is 0
Derive elastic collision in one dimension
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Formulas for elastic collision in one dimension
v1 = (m1 - m2)(u1)/(m1 + m2) + 2m2(u2)/(m1 + m2)
v2 = (m2 - m1)(u2)/(m1+m2) + (2m1)(u1)/(m1+m2)
Coeff of restitution formula
Gives a measure of the degree of restitution of a collision and is defined as ratio of magnitude of relative velocity of separation after collision to magnitude of relative velocity of approach before collison
e = |v1 - v2|/|u1 - u2|
