How do Newton's Laws work in these situations?

[vu10758]

1) A 5kg box is pulled by a force F horizontally (no angle). There is friction between the box and horizontal surface. Mu_k = .25 and Mu_s = .5. If F=20N find the magnitude of the friction force and the acceleration of the block.

I used the formula |f_k| = mu_k * |Normal force|

f_k = .25 * 9.8 * 5
f_k = 12.25 N

The correct answer is that the friction is 20 N, meaning that the block didn't move. Where did I go wrong?

2) A 5kg sled is pulled an an angle 5 degree above the horizontal. Friction between the sled and the snow is described by mu_k = .1 and mu_s = .15. What is acceleration of the sled?

The correct answer is 2.99 m/s^2

This is what I did.

I took the 20 N and multiply by cos (5 degree) to get 19.92.

|f_k| = mu_k * N
f_k = .1*5*9.8
f_k = 4.9

(19.92 - 4.9) / 5 = a
a = 3.004

Did I just round my answer differently or did I do something wrong?

3) A 2kg object is under the influences of several forces. Assume that the net force is constant. At t=0, the object's velocity is 3i + 2j and at t=4s its velocity is 11i - 14j . Find the magnitude and direction of net force acting on the object. Please explain this to me. I have no idea how to start.

Thanks in advance for your help.

 

[AussieDave]

Can you please tell me what Mu_k, Mu_s and |f_k| all mean? I'm doing similar stuff to this at the moment but I don't recognise those things you are using.

 

[vu10758]

Mu_k is the coefficient of kinetic friction
Mu_s is coefficient of static friction

|f_k| is kinetic friction
|f_s| is static friction

 

[AussieDave]

Oh okay gotcha. Yeah I actually probably can't help because I haven't yet delved into static and kinetic friction really. I have worked with simply friction before without determining differences between the two

 

[HallsofIvy]

Before the box moves, it is static friction that is important. You calculated the acceleration using kinetic friction. Go back and do it using static friction.

 

[vu10758]

Thanks for your help. Since the static friction is greater than the force pushing the object, the object will not move. Since 20N is applied on the object, the friction is also 20N according to Newton's Third Law. Am I correct?