Answer to Question #143703 in Physics for Sydney

Question

Roofers need to move equipment onto the roof of a building. They have a machine that will pull a platform at varying accelerations. The rope used to pull the platform will snap if a force of 5550 Newtons is exceeded. The platform itself has a mass of 50.0kg. The equipment has a mass of 475 kg. What is the maximum acceleration the machine could lift the equipment without snapping the rope?

Answer 1

In order to prevent the snap, the acceleration should be (accroding to the Newton's second law):

$$a\le\dfrac{F}{m}$$

where $F = 5550N$ is the force threshold, and $m = 50kg + 475kg = 525kg$ is the total mass of the platform and equipment. Thus, obtain:

$$a\le\dfrac{5550N}{525} = 10.6m/s^2$$

Answer. The maximum acceleration is 10.6 m*s^-2.