An untethered block sits on a flatbed truck as it accelerates up an incline that makes an angle of 15° with respect to the horizontal. if the truck speeds up at a rate less than 2.69 m/s2, the block remains on the truck. if the truck speeds up at a rate equal to or greater than this value, however, the block slides off the truck. what is the coefficient of static friction between the truck and the block?

The coefficient of static friction is 0.524

Solution:

As per the question:

Angle made with the horizontal,

Acceleration of the truck, a = 2.69

Now,

Forces are balanced along the x- direction:

When the block sits at rest and is about to slide:

             (1)

Also, static force of friction, :

where

N = mgcos

Thus

         (2)

Now, from eqn (1) and eqn (2):

Also,

a =

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)