Final answer:
The maximum load that can be lifted slowly at a constant speed by the rope is 4710 N. The maximum load that can be lifted by the rope with an acceleration of 4.00 m/s² is approximately 1177.5 kg.
Step-by-step explanation:
The maximum load that can be lifted slowly at a constant speed by the rope can be determined using the formula:
Maximum Load (force) = Tensile Stress x Cross-sectional Area
Given that the tensile stress is 6.00 x 10^6 N/m² and the cross-sectional area can be calculated using the formula for the area of a circle:
Area = π x (radius)²
Since the diameter is given as 1.0 mm, the radius will be 0.5 mm or 0.0005 m. Substituting these values into the formulas gives:
Area = π x (0.0005)² = 0.000785 m²
Maximum Load = 6.00 x 10^6 N/m² x 0.000785 m² = 4710 N
Therefore, the maximum load that can be lifted slowly at a constant speed by the rope is 4710 N.
To determine the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s², we need to consider the force required to accelerate the load. This can be determined using Newton's second law:
Force = Mass x Acceleration
Since the acceleration is given as 4.00 m/s², we can calculate the mass of the load using the formula:
Mass = Force / Acceleration
Given that the force is 4710 N, we can substitute these values into the formula to find:
Mass = 4710 N / 4.00 m/s² = 1177.5 kg
Therefore, the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s² is approximately 1177.5 kg.