1

W = F · Δr = FΔr cos θ[W] = [F][L] = M(L/T)²1 J = 1 kg·m²/s²

2

W = ∫rfri F(r) · drW = ∫xfxi F(x) dx =

3

W = ∫F dx = ∫mdvdtdx = ∫mv dvW = (1/2)mv²_f − (1/2)mv²_i = ΔKK = (1/2)mv²

4

W_g = mgd cos φv_f = v²_i ± 2gdW_a + W_g = ΔK = 0 ⇒ W_a = mgd

5

Fs = −kdWs = ∫xfxi (−kx) dx = (1/2)kx2i − (1/2)kx2f[k] = N/m = kg/s2

6

P_avg = WΔtP = dWdt = F · v1 W = 1 J/s,  1 kWh = 3.6 × 10⁶ J

7

ΔU = −W∮ F · dr = 0Wab,1 = −Wba,2 = Wab,2ΔU = −∫xfxi F(x) dx

8

U(y) = mgyU(x) = (1/2)kx²E_mec = K + UΔK + ΔU = 0v = 2gh

9

mgh = (1/2)mv² ⇒ v = 2ghv(y) = 2g(h₀ − y)

10

W = F(x)Δx = −ΔU(x)F(x) = −dU(x)dxU = (1/2)kx² → F = −kxU = mgy → F = −mg

11

(F − f_k)d = (1/2)mv² − (1/2)mv²₀W = Fd = ΔE_mec + ΔE_thΔE_th = f_kdW = ΔE = ΔE_mec + ΔE_th + ΔE_intP = dEdt