Physics and thanks for the help

Question

What applied horizontal forces is required to accelerate a 10-kg body along a horizontal surface with the acceleration of 2 m/s^2 if the coefficient of kinetic friction is 0.3?

Answer 1

Equations to know:

∑F = ma

F_friction = Nµ, where N is the normal force and µ is the coefficient of kinetic friction

The normal force is the force that the ground exerts on an object (usually just the weight of the object, unless the ground is at an angle): N = mg, where g is the acceleration of gravity (g = 9.8m/s^2)

Friction opposes the applied horizontal force so these two forces will have opposite signs:

∑F = F_applied - F_friction

We have m = 10kg, a = 2m/s^2 and µ = 0.3

Now plugging in our values we get:

F_applied - F_friction = ma ⇒ F_applied - Nµ = ma ⇒ F_applied - mgµ = ma ⇒ F_applied - 10*9.8*0.3 = 10*2

⇒ F_applied - 29.4 = 20 ⇒ F_applied = 49.4