Final answer:
To calculate the maximum force the motor should exert on an elevator's supporting cable with a mass of 5000 kg and maximum acceleration of 7.00×10⁰g, first compute the acceleration due to gravity and the net force needed for this acceleration. Then, add the weight of the elevator to find the total force the motor must exert. The total force comes out to be approximately 52483.5 N.
Step-by-step explanation:
The subject of the question is Physics, specifically related to dynamics and mechanical systems that involve forces, mass, and acceleration. The student is inquiring about designing an elevator and the maximum force the motor should exert on the supporting cable when the maximum acceleration is 0.070g (where g is the acceleration due to gravity, approximately 9.81 m/s²). To calculate the maximum force, we use the formula F = ma, where F is the force, m is the mass of the elevator, and a is the acceleration. However, the acceleration to be used in the formula is 0.070 times the acceleration due to gravity (g).
To find the maximum force, we first calculate the acceleration the elevator experiences, which is 0.070 × 9.81 m/s² = 0.6867 m/s². Then using the mass of the elevator, which is 5000 kg, we can calculate the force as follows:
F = m × a
F = 5000 kg × 0.6867 m/s²
F = 3433.5 N
This is the net force needed to achieve the maximum acceleration. However, since the elevator also has to overcome the force of gravity acting down, the total force the motor must supply is the sum of the net force and the weight of the elevator (mg). Therefore:
Total force = F + mg
Total force = 3433.5 N + (5000 kg × 9.81 m/s²)
Total force = 3433.5 N + 49050 N
Total force = 52483.5 N
This is the maximum force the motor should exert on the supporting cable.