T1 cos 28 = T2 cos 16
(no net horizontal force)
T1 + T2 = 46
for vertical equilibrium
A 46−N lithograph is supported by two wires. One wire makes a 28° angle with the vertical and the other makes a 16° angle with the vertical. Find the tension in each wire.
2 answers
28o W. of N. = 118o CCW from +x-axis.
16o E. of N. = 74o CCW from +x-axis.
T1*Cos118 = -T2*Cos74.
T1 = -T2*Cos74/Cos118 = 0.587T2.
T1*sin118 + T2*sin74 = -(-46),
0.883T1 + 0.961T2 = 46,
0.883(0.587T2) + 0.961T2 = 46,
0.518T2 + 0.961T2 = 46, T2 = 31.1 N.
T1 = 0.587*T2 = 0.587*31.1 = 18.2 N.
16o E. of N. = 74o CCW from +x-axis.
T1*Cos118 = -T2*Cos74.
T1 = -T2*Cos74/Cos118 = 0.587T2.
T1*sin118 + T2*sin74 = -(-46),
0.883T1 + 0.961T2 = 46,
0.883(0.587T2) + 0.961T2 = 46,
0.518T2 + 0.961T2 = 46, T2 = 31.1 N.
T1 = 0.587*T2 = 0.587*31.1 = 18.2 N.
1 answer