Holding a long rope by its upper end, you lower it onto a scale. The rope has a mass of 0.160 kg per meter of length, and is lowered onto the scale at the constant rate of 1.30 m/s.

(1) Calculate thrust.

(2) At the instant when the amount of rope at rest on the scale has a weight of 2.74 N , does the scale read 2.74 N, more than 2.74 N, or less than 2.74 N?

Not sure how to set this problem up.

To solve this problem, we need to understand the concepts of thrust and weight.

1) Thrust is the force exerted by an object in a fluid (such as air or water) in the opposite direction to its motion, typically caused by the pressure difference between the front and back sides of the object. In this case, the thrust is the force exerted by the rope as it is being lowered onto the scale.

To calculate the thrust, we need to find the rate of change of momentum of the rope. The rate of change of momentum is given by the equation:

Thrust = mass × acceleration

In this case, the mass of the rope is given per meter of length, so to find the total mass of the rope, we need to multiply the mass per meter by the length of the rope that is on the scale. The acceleration of the rope is the rate at which it is being lowered, which is 1.30 m/s.

Hence,

Thrust = (mass per meter) × (length of the rope on the scale) × (acceleration)

2) Now, let's analyze the second part of the question. At the instant the weight of the rope on the scale is 2.74 N, we need to determine whether the scale will read exactly 2.74 N, more than 2.74 N, or less than 2.74 N.

To do this, we need to consider the weight of the rope that is already on the scale and the weight of the rope that is still being lowered down. The weight of the portion that is on the scale is its mass times the acceleration due to gravity. The weight of the remaining portion, which is still being lowered, is its mass times the acceleration due to gravity.

If the scale reads more than 2.74 N, it means that the weight of the portion on the scale plus the weight of the remaining portion is greater than 2.74 N. If it reads less than 2.74 N, then the total weight is less than 2.74 N. And if it reads exactly 2.74 N, then the total weight is 2.74 N.

Now, armed with these explanations, you should be able to set up and solve the problem!