A 65-kg box is places on the sidewalk. Laprunda pushes the box to the left with 550 N of force. Does the box move?

Concept used:

We will Use Newton's second law of motion to solve this Question

Yes, the box will move by following the newton's second law of motion

Solving for the acceleration of the Box:

Assuming that the sidewalk is frictionless

According to newton's second law of motion:

F = ma

we are given that:   F = 550 N   and   m = 65 kg

replacing the variables

550 = 65 * a

a = 8.5 m/s² (approx)

Therefore, the box will have a constant acceleration of 8.5 m/s² for the time period when the force is applied

We can't tell from the given information.

If the box were on ice or an air-hockey table, then just about ANY force could move it, no matter how small.

If the box were on mud or molasses, then just about NO force could move it, no matter how great.

The difference is the friction between the box and whatever it's on.

The force that resists motion of the box is (weight) x (coefficient of friction). We don't know the coefficient of friction between the box and the sidewalk.

The weight of the box is (mass) x (gravity).

Weight = (65 kg) x (9.8 m/s²)  =  637 Newtons.

Friction = (637N) x (coefficient of friction)

The box moves IF Lapunda's push is greater than the force of friction.

550N > (637N) x (μ)   <-- that's a 'mu', usually used for coefficients

Now divide each side by (637N): . . . . (550/637) > μ

μ < 0.863

-- If the coefficient of friction between the box and sidewalk is less than 0.863, then the box moves.

-- If the coefficient of friction between the box and sidewalk is greater than 0.863, then the box doesn't move.

That's why we sand and polish sliding surfaces, and slather them with oil.  It's to reduce their  μ .