Question

You must push a crate across a floor to a docking bay. The crate weighs 198 N. The coefficient of static friction between crate and floor is 0.530, and the coefficient of kinetic friction is 0.260. Your force on the crate is directed horizontally. (a) What magnitude of your push puts the crate on the verge of sliding? (b) With what magnitude must you then push to keep the crate moving at a constant velocity? (c) If, instead, you then push with the same magnitude as the answer to (a), what is the magnitude of the crate's acceleration?

Answer 1

Answer:

a) 104.94 N,   b)  F = 51.48 N ,  c) a = 2.65 m / s²

Explanation:

We apply Newton's second law to solve the problem, in the attached you can see a free body diagram

X axis

     F - fr = ma

     fr = μ N

    F = μ mg + m a

    F = m (μ g + a)

Axis y

   N- W = 0

   N = w = mg

a) The force just before starting the movement, in this case the friction force is static, in this case the acceleration is zero

   F = fr

   F = μ mg

   F = 0.530 198

   F = 104.94 N

b) When the box is already moving the friction force changes the dynamic friction force and if the box moves with constant speed the acceleration is zero

   F = fr

   F = 0.260 198

   F = 51.48 N

c) In this case F is 104.95 N, but the friction force is 51.48 N

   W = mg

   m = W / g

   m = 198 /9.8

   m = 20.2 kg

   F-fr = ma

   a = (104.98 - 51.48) /20.2

    a = 2.65 m / s²