Question

reselasie3. An object of mass 900 kg is hanging from a ceilingby means of two strings. The first string (7₁) makes anangle of 40 degree with the horizontal-right. The second string(T₂) makes an angle of 20 degree with the horizontal-left.Calculate the tension in the first string (7₁) (2 point)A. O12034.001 NB. O14675.062 NC. 5790.32 ND. 09570.261 NE. 13316.872 N

Answer 1

First, find the weight of the object.

W = m g = 900 x 9.8 = 8,820 N

T2x = -t2 cos 20

t1 x = t1cos 40

mgx= 0

T2y= t2 sin 20

t1y= t1 sin 40

mgy= - mg

X and y components of resultant (R)

Rx = t1x -t2x + mgx

Rx= -t2 cos 20 + t1cos 40 (3)

Ry = t2 sin 20 + t1 sin 40 - mg(2)

Rx, and Ry = 0

0 = -t2 cos 20 + t1cos 40 (3)

0= t2 sin 20 + t1 sin 40 - mg (4)

Solve (3)

0 = -t2 cos 20 + t1cos 40

t2 cos 20 = t1 cos 40

t2 = t1 cos40/cos20

t2 = 0.815 t1

Substitute t2 in 4

0 = t2 sin 20 + t1 sin 40 - mg

0 = (0.815 t1) sin 20 + t1 sin 40 - 8,820

0= t1 ( 0.815 sin 20 + sin 40 ) -8820

0 = 0.921 t1 -8820

8820 = .921 t1

t1 = 8820/0.921

t1= 9570.261N (option D)