Question

Three strings are tied together as shown to the right and placed on a lab table. A different mass is suspended from the free end of each of the three strings after the free ends are draped over pulleys (see the diagram below); m2 is 145 grams and m3 is 210 grams. Angle has a value of 65.0 degrees and angle β has a value of 38.7 degrees . What is the value of m1 if the knot connecting the three strings is at equilibrium?

The answer is 225 g (0.225 kg), but I'm not sure how to solve this. Can anyone help?

Answer 1

225 g

Step-by-step explanation:

in order to be at equilibrium:

m2x + m3x = m1

m2x = m2 × cos α

= 145 × cos 65.0°

= 61.28 g

m3x = m3 × cos β

= 210 × cos 38.7°

= 163.89 g

m1 = m2x + m3x

= 61.28 + 163.89

≈ 225 g