How much work would it take to horizontally accelerate an object with a mass of #4 kg# to #2 m/s# on a surface with a kinetic friction coefficient of #3 #?
1 Answer
Answer:
Explanation:
We're asked to find the work necessary to accelerate a
To do this, we'll use the equation
where

#f_k# is the magnitude of the retarding friction force 
#mu_k# is the coefficient of kinetic friction (#3# ) 
#n# is the magnitude of the normal force, which since the plane is horizontal is equal to
#n = mg = (4color(white)(l)"kg")(9.81color(white)(l)"m/s"^2) = 39.24# #"N"#
The kinetic friction force is thus
This means a force of at least
The work will be the same regardless of the force here; let's say the applied force is
The magnitude of the acceleration is
Using kinematics, we can find the displacement
It starts from rest, so we have
Using
we have