CK-12-Physics - Intermediate

http://www.ck12.org Chapter 5. Forces in Two Dimensions

FIGURE 5.25

θ 1 = 45 ◦

θ 2 = 30 ◦

Mg= 800 N

FindT 1 andT 2

The solution requires solving a set of simultaneous equations.

First, we find the components of vectorsT 1 andT 2.

T 1 x=T 1 sin 45◦and T 1 y=T 1 cos 45◦

T 2 x=T 2 sin 30◦and T 2 y=T 2 cos 30◦

Next we apply Newton’s Second Law.

∑Fx:T 2 sin 30

◦−T

1 sin 45

◦= 0

∑Fy:T^2 cos 30

◦−T 1 cos 45◦= 800

The first equation can be quickly simplified to giveT 2 =

√

2 T 1 .T 2 is then substituted in the second equation andT 1
is found. OnceT 1 is found,T 2 can easily be computed usingT 2 =

√

2 T 1.