directions: create a model to help you solve the problem below. all models must include an explanation…

Explanation:

Step 1: Recall Newton's Second Law

Newton's second law states ( F_{net} = ma ), where ( F_{net} ) is the net force, ( m ) is the mass, and ( a ) is the acceleration. For the load, the forces acting on it are the tension ( T ) upward and the weight ( mg ) downward. So, ( T - mg = ma ), which can be rearranged to ( T = m(g + a) ). Given ( m = 10 , \text{kg} ), ( g = 9.8 , \text{m/s}^2 ), and ( a ) between ( 1 , \text{m/s}^2 ) and ( 2 , \text{m/s}^2 ). Let's take the maximum acceleration ( a = 2 , \text{m/s}^2 ) (to find the maximum tension needed). Then ( T = 10(9.8 + 2) = 10 \times 11.8 = 118 , \text{N} ). But we have an applied force ( F ) less than ( 35 , \text{N} ). In a pulley system, the tension is related to the applied force by the number of supporting ropes ( n ), so ( T = nF ) (assuming ideal pulleys, massless string, etc.). We need to find ( n ) such that ( nF \geq T ) and ( F < 35 , \text{N} ). Let's solve for ( n ): ( n \geq \frac{T}{F} ). If ( F = 35 , \text{N} ), ( n \geq \frac{118}{35} \approx 3.37 ). So we need at least 4 supporting ropes (since ( n ) must be an integer).

Step 2: Design the Pulley System

We can use a combination of fixed and movable pulleys. Let's use 2 movable pulleys and 2 fixed pulleys (total of 4 pulleys, which is within 3 - 5). The arrangement: Attach two fixed pulleys to the beam. Attach two movable pulleys to the load. The string is attached to the beam, goes around a movable pulley, then a fixed pulley, then the other movable pulley, then the other fixed pulley, and the applied force is at the end. The number of supporting ropes ( n = 4 ). Now, check the applied force: ( F = \frac{T}{n} ). For ( a = 2 , \text{m/s}^2 ), ( T = 118 , \text{N} ), so ( F = \frac{118}{4} = 29.5 , \text{N} ), which is less than ( 35 , \text{N} ). For ( a = 1 , \text{m/s}^2 ), ( T = 10(9.8 + 1) = 108 , \text{N} ), ( F = \frac{108}{4} = 27 , \text{N} ), also less than ( 35 , \text{N} ). We can also use a wooden plank (optional) to attach pulleys if needed, but in this case, attaching the fixed pulleys to the beam and movable to the load works. The model includes: 10 - kg load, massless string, 2 fixed and 2 movable pulleys (total 4, within 3 - 5), and 0 wooden planks (or 1 if we want to attach pulleys to it, but not necessary here). The explanation is based on Newton's second law and pulley mechanics, relating tension, applied force, and number of supporting ropes.

Answer:

A pulley system with 2 fixed pulleys (attached to the beam) and 2 movable pulleys (attached to the 10 - kg load), connected by a massless string. The applied force at the end of the string will be less than 35 N (e.g., 27 - 29.5 N) to lift the load with an acceleration between ( 1 , \text{m/s}^2 ) and ( 2 , \text{m/s}^2 ). The number of supporting ropes ( n = 4 ), so ( T = nF ) and ( T = m(g + a) ) ensures the acceleration requirement is met.