Δp/Δt = −ΔEP/Δs why a negative?

[S1CkFiSh]

Why is there a minus sign in the formula Δp/Δt = −ΔEP/Δs? Is it because the objects are accelerated toward or away from a higher potential, or is it something else? If anyone could help me, thank you!

 

[Andrew Mason]

Why is there a minus sign in the formula Δp/Δt = −ΔEP/Δs? Is it because the objects are accelerated toward or away from a higher potential, or is it something else? If anyone could help me, thank you!

If energy is conserved, there is no overall change in energy. So, when potential energy is lost, the same amount of kinetic energy is gained and vice versa: ΔKE + ΔPE = 0 or ΔKE = - ΔPE.

Since the magnitude of the force can be thought of as the rate of change of kinetic energy with distance (ie since ΔKE = work done = |F|Δs, |F| = ΔKE/Δs -- Δs being the change in distance in the direction of the force) and ΔKE = -ΔPE, then |F| = -ΔPE/Δs.

AM