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two ropes support a load of 663 kg. the two ropes are perpendicular to each other, and the tension in the first rope is 1.94 times that of the second rope. find the tension in the second rope. the acceleration of gravity is 9.8 m/s 2 . answer in units of n.

Respuesta :

Formulas for the balancing of forces

Examine the force diagram in the graph that is attached:

∑Fx=0

T1sen - T2cos = 0 Equation

∑Fy=0

T1cos ∝ + T2sin ∝ - W = 0. Equation(2)

forces in the x and y directions,

Horizontal movement

T1*CosA=T2*Cos(90-A)

Vertical Movement

m*g = T1*SinA + T2*Sin(90-A) (2)

We also know that T1=1.91 and T2 (3)

Thus, the final equations are

T1*CosA=T2*Cos(90-A)

A=62.365235 degrees using (2) and substituting a value for (3)

460*9.8 = 1.91*T2 *Sin(62.365235) + T2 *Cos(62.365235)

T2 = 4508 / (2.1559) = 2090.96 N

T1 = 1.91*T2 = 3993.737 N

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