Forces & Friction: Calculating Normal Force & Horizontal Force

[santoki]

Homework Statement

A man is pulling a 40.0 kg crate across a level floor with a horizontal force, and the coefficient of kinetic friction is μk = 0.59 for the crate and the floor.

14. What is the normal force acting on the box?
a) 231 N
b) 340 N
c) 196 N
d) 392 N

15. What horizontal force must the man apply to get the crate to accelerate at 2.0 m/s2 ?
a) 311 N
b) 231 N
c) 81 N
d) 40 N

2. The attempt at a solution

For 14:
N = mg = (40.0)(9.8) = 392N

For 15:
N-F_x = ma_x
392 - F_x = (40.0)(2.0)
F_x = 312N

but there's no 312N there and I didn't even incorporate the μk?

 

[Chestermiller]

Did you draw a free body diagram? Is N a horizontal force or a vertical force?

Chet

 

[santoki]

Did you draw a free body diagram? Is N a horizontal force or a vertical force?

Chet

N is a horizontal force.

 

[haruspex]

N is a horizontal force.

No, it's a vertical force, the vertical component of the reaction from the floor.
What, then, is the frictional force?
What is the relationship between the frictional force, the applied force, and the resulting acceleration? (Your equation was wrong.)