Question

energy of an object as it moves form one point to another

Answer 1

Do you mean how the energy of an object changes when it moves from one point to another? Here are the main ideas and formulas you can use:

1. Work (general definition)
- Work done by a force F when the object moves along a path from r1 to r2:
W = ∫_{r1}^{r2} F · dr
- Units: joules (J).

2. Kinetic energy and the work–energy theorem
- Kinetic energy: K = 1/2 m v^2.
- Work–energy theorem (net work → change in kinetic energy):
W_net = ΔK = K_2 − K_1.

3. Potential energy and conservative forces
- For a conservative force, you can define a potential energy U such that W_conservative = −ΔU.
- Common potentials:
- Gravity (near Earth): U = m g y so ΔU = m g Δy.
- Spring: U = 1/2 k x^2.
- If only conservative forces act, mechanical energy is conserved:
K_1 + U_1 = K_2 + U_2.

4. Non-conservative forces (friction, applied forces)
- Work done by non-conservative forces W_nc changes the total mechanical energy:
W_nc = Δ(K + U) = (K_2 + U_2) − (K_1 + U_1).
- Rearranged: K_2 + U_2 = K_1 + U_1 + W_nc.

5. Practical steps to compute energy change between two points
- Identify forces doing work (conservative vs non-conservative).
- Compute W for each force (or use ΔU for conservative forces).
- Use W_net = ΔK and/or W_nc = Δ(K+U) to find the desired unknown(s).

6. Quick example (object falling from height h, no air resistance)
- Initial: K_1 = 0, U_1 = m g h. Final at ground: U_2 = 0.
- Mechanical energy conserved → K_2 = m g h, so 1/2 m v^2 = m g h → v = sqrt(2 g h).

If you tell me the forces involved, the start and end positions (or heights), and whether there’s friction or applied work, I can compute the energy change for your specific case.