A crate resting on a horizontal floor (\muμs = 0.75, \muμk = 0.24 ) has a horizontal force F = 93 Newtons applied to the right. This applied force is the maximum possible force for which the crate does not begin to slide. If you applied this same force after the crate is already sliding, what would be the resulting acceleration (in meters/second2) ?

The  acceleration is  

Explanation:

From the  question we are told that

      The  coefficient of kinetic friction is  

       The coefficient of static friction is  

       The horizontal force is

Generally the static frictional force is  mathematically represented as

The  static frictional force is the equivalent to the maximum possible force for which the crate does not begin to slide So

=>      

=>        

substituting values  

When the crate is already sliding the frictional force is

substituting values  

Now the net force when the horizontal force is applied during sliding is  

substituting values  

This  net force is mathematically represented as

Where a is the acceleration of the crate

So  

Power = 377.35 W or Power = 0.5065 hp

Explanation:

Given:

Number of steps, n = 1576

height of each step, h = 0.20 m

Total height achieved, H = nh = 1576 × 0.20 = 315.2 m

Mass of the runner, M = 70.0 kg

Total time taken, t = 9 minutes 33 seconds = (9 × 60) + 33 = 573 seconds

Now, the potential energy gained by the runner,

E = MgH

where, g is the acceleration due to the gravity

on substituting the values in the above formula, we get

E = 70 × 9.8 × 315.2

or

E = 216227.2 J

also,

Energy = Power × time

therefore,

Power = Energy/time

or

Power = 216227.2 J / 573

or

Power = 377.35 W

Now,

745 watt = 1 hp

or

1 watt = 1/745 hp

thus,

Power = 377.35 W = 337.35 × (1/745) hp

or

Power = 0.5065 hp