Question

Expliquem Por favor!!

Answer 1

Resposta:

Explicação passo-a-passo:

Para ambos os casos pode ser utilizado a lei geral dos cossenos no cálculo vetorial.

Desta forma:

a)

$F^{2} _{r} = F^{2} _{1} + F^{2} _{r} + 2F _{1}2F _{2}cos\beta \\F^{2} _{r} = 10^{2} + 10^{2} + 2(10)(10)cos0^{0} \\F^{2} _{r} = 100 + 100 + 200(1)\\F^{2} _{r} = 400\\F _{r} = \sqrt{400} \\F _{r} = 20 N$

b)

$F^{2} _{r} = F^{2} _{1} + F^{2} _{r} + 2F _{1}2F _{2}cos\beta \\F^{2} _{r} = 10^{2} + 10^{2} + 2(10)(10)cos180^{0} \\F^{2} _{r} = 100 + 100 + 200(-1)\\F _{r} = 0$

c)

$F^{2} _{r} = F^{2} _{1} + F^{2} _{r} + 2F _{1}2F _{2}cos\beta \\F^{2} _{r} = 10^{2} + 10^{2} + 2(10)(10)cos90^{0} \\F^{2} _{r} = 100 + 100 + 200(0)\\F^{2} _{r} = 200\\F _{r} = \sqrt{200} \\F _{r} = 14,14 N$

d)

$F^{2} _{r} = F^{2} _{1} + F^{2} _{r} + 2F _{1}2F _{2}cos\beta \\F^{2} _{r} = 10^{2} + 10^{2} + 2(10)(10)cos60^{0} \\F^{2} _{r} = 100 + 100 + 200(1/2)\\F^{2} _{r} = 300\\F _{r} = \sqrt{300} \\F _{r} = 17,32 N$

e)

$F^{2} _{r} = F^{2} _{1} + F^{2} _{r} + 2F _{1}2F _{2}cos\beta \\F^{2} _{r} = 10^{2} + 10^{2} + 2(10)(10)cos120^{0} \\F^{2} _{r} = 100 + 100 + 200(-1/2)\\F^{2} _{r} = 100\\F _{r} = \sqrt{100} \\F _{r} = 10 N$