01/ 09/ '09

1.65 SEARS ZEMANSKY pág. 65

|A|= A= 100 N
|B|= B= 80 N
|C|= C= 40 N

¿Cuál es la fuerza resultante R?
R= A + B + C

A = Ax + Ay
B = Bx + By
C = Cx + Cy

R = Ax + Ay - Bx + By - Cx - Cy
R = Axi + Ayj - Bxi + Byj - Cxi - Cyj
R = (Ax-Bx-Cx)i +(Ay+ By- Cy)j

α y β = 30º γ = 53º

sen α = Ay/ A
Ay= A sen α
Ay = 50 N

cos α = Ax/ A
Ax= A cos α
Ax = 86.6 N

sen β = Bx/ B
Bx= B sen β
Bx = 40 N

cos β = By/ B
By= B cos β
By = 69.28 N

sen γ = Cy/ C
Cy = C sen γ
Cy = 31. 94 = 32 N

cos γ = Cx/ C
Cx = C cos γ
Cx = 24.07 N

Σ Vx = (86.6 - 40 - 24.07) N
Σ Vx = 22.53 N

Σ Vy = (50 + 69.28 -32)N
Σ Vy = 87.28 N


R = 22.53 i + 87.28j
R = (22.53)² + (87.28)²
R = 90.14 N

Tan φ = Ry/ Rx
φ = Tan-1 = 72.52º

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a = Δv / Δt = Δt = Δv/a
implica

r= r0 + V0 (t- t0)+ 1/2 a (t- t0)²

^{para obtener}

V^{2 =}V0² + 2a Δr

mediante integración

adr = vdv
a ∫ dr = ∫ vdv
a r | r-r0 = v²/v | v-v0
ar- ar0 = 1/2 (v²- v0^{2 )}

2a (r-r0) = v²- v0²

V^{2 =}V0² + 2a Δr

donde Δr = r-r0