Calculating the Distance a Box Moves on a Moving Belt Without Slipping

[Xamfy19]

I have no clue how to start solving the question as follows:
A box is dropped onto a conveyor belt moving at 1.7 m/s. If the coefficient of friction between the box adn the belt is 0.7, what distance doest the box move before it moves without slipping? (g = 9.8 m/s)

What is the horizontal force to move the box on the belt?

Thanks alot.

 

[gnome]

What is the horizontal force to move the box on the belt?

Friction.

 

[Xamfy19]

Why it stop slipping? How should I start my formula? Thanks

 

[gnome]

What does an object do when a force acts on it?

 

[Xamfy19]

acceleration

It should create acceleration. Now, I have just tried to solve it and the following is the formula I used.

mg(0.7) = ma, a = 6.86. I assumed this was the acceleration responsible for moving box. Then, I use V = Vo - at
0 = 1.7 - 6.86t, t = 0.2478, substituted into d = Vot - 0.5 a t^2,
d= 1.7t - 0.5 * 6.86 * (0.2478)^2
= 0.2106 m
Is there anything (step) I missed or made mistake?

Thanks alot

 

[gnome]

Looks OK to me.

Although I would have written
v_f = v₀ + at
and let v₀=0 and v_f=1.7 m/s

Then d = 0 + .5at²

Gives the same answer.