A mass of 9.5 kg hangs from 2 ropes. If α = 41.0 deg. and β = 52.0 deg., what is the tension in rope 1?

electron1

The sum of the vertical components of the tension forces is equal to the object’s weight. The two horizontal forces are equal in magnitude. Weight = 9.5 * 9.8 = 931 N Eq#1: T1 * cos 41 + T2 * cos 52 = 931 T1 * sin 41 = T2 * sin 52 Eq#2: T2 = T1 * sin 41 ÷ sin 52 Substitute this for T2 in the first equation. T1 * cos 41 + T1 * (sin 41 ÷ sin 52) * cos 52 = 931 T1 = 931 ÷ (cos 41 + (sin 41 ÷ sin 52) * cos 52) This is approximately 735 N. To check this answer, let’s substitute in second equation. T2 = [931 ÷ (cos 41 + (sin 41 ÷ sin 52) * cos 52)] * sin 41 ÷ sin 52 This is approximately 611 N. Let use these numbers in the first equation. Eq#1: 735 * cos 41 + 611 * cos 52 This rounds to 931 N. This proves that both answers are correct. I hope this is helpful for you.

RealPro

Good thing there's google huh?

Sofia

Would love to help but I’m terrible at maths, sorry