Final answer:
To rank ropes by the force exerted on a crate to its left, start with the closest rope, assuming a straight line pull. Tension is equal along the rope, and vector addition helps understanding the cumulative force. Experiments demonstrate force standards and the relationship between weights and stretch in materials.
Step-by-step explanation:
To rank the ropes based on the force each exerts on the crate immediately to its left, we must apply the concept of vector addition in physics. Assuming that the ropes are pulling with different tensions and there are multiple ropes, we can ascertain that the rope closest to the crate would exert the greatest force as all the subsequent forces are additive upon this rope due to their direction being towards the crate. The tension in a perfectly flexible rope, according to Newton's third law, is the same throughout its length if the weight of the rope is negligible. Therefore, the ranking of ropes based on the force exerted will start with the rope closest to the crate and decrease moving away from it, assuming other factors like angles or additional forces are not in play.
As for the baby being weighed, the mass can be derived from the scale reading by using the acceleration due to gravity to convert from weight to mass: (a) mass of infant and basket = 55 N / 9.81 m/s2. The tensions T₁ and T₂ would be equal to the scale reading of 55 N if the system is in equilibrium and the mass of the rope is negligible, as indicated in the problem statement. For the tug-of-war question, if both teams exert the same average force, the total force each rope exerts would be determined by the sum of forces from the team members on each side. In the experiment with the rubber bands, the amount of stretch will increase in direct proportion to the number of weights added. Meanwhile, in cases such as a car being pulled out of the mud, the force exerted on the car can be computed using trigonometry, considering the angle at which the force is applied.