The James Bond director is still disappointed with the stunts you've worked on, so he's come up with something else. He wants Bond to fight a henchman on the roof of a moving train. The coefficient of static friction between the actors' shows and the train is 0.84.What is the maximum acceleration the train could have without causing the actors to slide off?

The maximum acceleration the train can have without causing any actors to slide off = 8.232 m/s²

Explanation:

As long as the force of the moving train (on the actors), that causes acceleration doesn't exceed the frictional force between the shoes of the actors and the train, the actors will not slide off.

The maximum acceleration is the acceleration that corresponds to just when this acceleration causing force matches the frictional force.

Frictional force per actor = μN

where N is the normal reaction of the train on each actor and it is equal to mg, the weight of each actor.

The force causing acceleration = ma

So, ma = μ mg

Such that the masses can cancel out

a = μ g = 0.84 × 9.8 = 8.232 m/s²

Therefore, the maximum acceleration the train can have without causing any actors to slide off = 8.232 m/s²