Basic Physics

# Particles in two-dimensional equilibrium – application of Newton’s first law problems and solutions

1. Find the tension force T1, T2, and T3. Ignore cord’s mass.

Solution

(a) Free-body diagram for object (b) Free-body diagram for cord

Apply the Newton’s first law on the object :

ΣFy = 0

T1 – w = 0

T1 = w = m g

T1 = (5 kg)(9.8 m/s2)

T1 = 49 kg m/s2

T1 = 49 N

Apply Newton’s first law on the cord :

Fx = 0

T3x – T 2x = 0

T3 cos 30o – T2 cos 40o = 0

0.87 T3 – 0.77 T2 = 0

0.87 T3 = 0.77 T2

T2 = 0.87 T3 / 0.77 = 1.1 T3 ———- Equation 1

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——

Fy = 0

T3y + T2y – T1y = 0

T3 sin 30o + T2 sin 40o – T1 = 0

0.5 T3 + 0.64 T2 – 49 N = 0 ———- Equation 2

Substituting T2 in the equation 2 into the equation 2 :

0.5 T3 + 0.64 (1.1 T3) – 49 N = 0

0.5 T3 + 0.70 T3 – 49 = 0

1.2 T3 – 49 = 0

1.2 T3 = 49

T3 = 49 / 1.2

T3 = 41 N

———

T2 = 1.1 T3

T2 = (1.1)(40.8 N)

T2 = 45 N

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