University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

380

Pages:

5
Author:

Jabin F.

#Potential Energy for some standard cases: 1. Gravitational Potential Energy near Earth's surface: U = -∫F.dl + C = -∫(mg)(-dz) + C = ∫mg dz + C = mgz + C U = mgz 2. Simple Pendulum (Potential Energy): Firstly we have to decide a reference point from where potential energy is taken as zero. Case I: If P.E. is zero at the point of suspension level. U = 0 Case II: If P.E. is zero at the lowest point. h = L - Lcosθ U = mgh = mgL(1-cosθ) 3. Gravitational Potential Energy of two masses (spherical): U = -∫F.dl + C = -∫(-Gm₁m₂/r²)dr + C = ∫(Gm₁m₂/r²)dr + C = -(Gm₁m₂/r) + C Electrostatic Potential Energy for two point/spherical charges: U = (kQ1Q2)/r + C Spring Potential Energy: U = -∫F.dl + C = -∫(-kx)(dx) + C = ½kx² + C Example: Suppose two masses connected by a single spring. x1, x2 are the displacement of two masses from their respective equilibrium positions. Then find out P.E. Solution: U = ½k(x₁ - x₂)² Q: Write the potential energy of the system. system with two springs and two masses Solution: U = ½k₁(x₁²) + ½k₂(x₂²) + ½k₃(x₁ - x₂)² Q: Write P.E. of particle moving in an xyplane Solution: Example: For a particle moving on xy-plane, x = 4t, y = x². What is the potential energy? (Unit mass particle)