Final answer:
To find the missing tension T2, we use equilibrium conditions and Newton's second law, where the upward tension forces must equal the downward weight forces. Tension T1 is given as 900 N, and the weights of the masses can be calculated using W = mg. Equations based on the forces' equilibrium help solve for the unknown tension T2.
Step-by-step explanation:
To find the missing tension T2 in the scaffold cable using F=0, we need to apply Newton's second law and the notion that the forces must be in equilibrium for a stationary system, meaning that the net force Fnet equals zero. When we have a system of cables supporting masses, the sum of the tensions must counteract the weight of the masses for the system to be in equilibrium.
To calculate the tensions, we must know the weight of the masses involved. Weight can be found using the formula W = mg where m is mass and g is the acceleration due to gravity (approximately 9.8 m/s²). For a 80 kg mass, the weight W would be 80 kg * 9.8 m/s² = 784 N. For a 50 kg mass, the weight would be 490 N, and for a 20 N mass, the weight is already given as 20 N.
Knowing T1 (900 N) and the weights, we can set up equations based on the equilibrium condition that the sum of the upward forces (tension forces) must equal the sum of the downward forces (weights of the masses). For example, if a system includes only T1 and the weight of an 80 kg mass, then T1 + T2 = 784 N, and we can solve for T2.