# Calculus/ Vectors

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A 10kg mass is supported by two strings of length 5 m and 7 m attached to two points in the ceiling 10 m apart. Find the tension in each string.

Help will be much appreciated! :)

• Calculus/ Vectors -

first draw a position diagram, a horizontal line 10 m, and two sides of 5 m and 7 ml to get triangle ABC
where b = 10, a=7, and c=5

by the cosine law,
5^2 = 10^2 + 7^2 - 2(10)(7)cosC
cosC = 124/140
angle C = 27.66°

by the Sine Law
sinA/7 = sin27.66/5
angle A = 40.54

now draw a vector diagram, triangle PQR
where PR = 10 and a vertical line, P above R
PR represents the 10 kg mass

Using the above results,
angle P = 62.34
angle Q = 40.54+27.66 = 68.20
angle R = 49.46

by sine law:
PQ/sin 49.46 = 10/sin68.20
PQ = 8.18

QR/sin62.34 = 10/sin68.2
QR = 9.54

the tension is the 7 m string is 8.18 kg
the tension in the 5 m string is 9.54 kg

check my arithmetic

draw PQ parallel to BC and QR parallel to AB
angle QPR = 90-27.66 = 62.34°

• retyped - Calculus/ Vectors -

the last two line got displaced, should have been:

first draw a position diagram, a horizontal line 10 m, and two sides of 5 m and 7 ml to get triangle ABC
where b = 10, a=7, and c=5

by the cosine law,
5^2 = 10^2 + 7^2 - 2(10)(7)cosC
cosC = 124/140
angle C = 27.66°

by the Sine Law
sinA/7 = sin27.66/5
angle A = 40.54

now draw a vector diagram, triangle PQR
where PR = 10 and a vertical line, P above R
PR represents the 10 kg mass

draw PQ parallel to BC and QR parallel to AB
angle QPR = 90-27.66 = 62.34°

Using the above results,
angle P = 62.34
angle Q = 40.54+27.66 = 68.20
angle R = 49.46

by sine law:
PQ/sin 49.46 = 10/sin68.20
PQ = 8.18

QR/sin62.34 = 10/sin68.2
QR = 9.54

the tension is the 7 m string is 8.18 kg
the tension in the 5 m string is 9.54 kg

check my arithmetic

• Calculus/ Vectors -

Hey the guy above is totally right. Except for the fact that is screwed up the Lenght of PR. To get the right answer you have to do 10kg * 9.8N = 98N. Which is the length of PR. Now use 98 with sine law as Rimey did above and you shall get 80 and 94 for your two tensions.