Finding acceleration of an object (with friction)

[Joe26]

Homework Statement

A 1,300-N crate is being pulled across a level floor at a constant speed by a force of 310 N at an angle of 20.0° above the horizontal. If coefficient of kinetic friction is 0.207, find the acceleration of the crate.

Homework Equations

Fk= (uk)(N)
F=ma

The Attempt at a Solution

Fx= 310cos20
Fy= 310sin20

N=1300-310sin20

Fk=(uk)(N) = (0.207)(1300-310sin20) = 247.15 N

sumFx= Fx-Fk =310cos20-247.15 = 44.15 N

F=ma=44.15
a=44.15/1300 =0.0340 m/s^2

Answer says a=0.331

Can someone point out what I did wrong? Thanks

 

[SammyS]

Doesn't gravity exert a force in the y direction, contributing to F_y ?

The F_y you have is downward. Do you want that to be negative ?

 

[Joe26]

im not sure if I quite follow. Yes, force of gravity (1300N) is exerted in the y-direction:

F1y= 310sin20
N=1300-310sin20
sumFy=N+F1y-1300N=0

I'm not sure what is wrong. Can someone help me out?

 

[Doc Al]

The applied force is downward:

a force of 310 N at an angle of 20.0° below the horizontal.

 

[Joe26]

sorry that should be above the horizontal

 

[Doc Al]

F=ma=44.15
a=44.15/1300 =0.0340 m/s^2

1300 N is the weight of the crate, not its mass.

 

[Joe26]

so, how would i be able to find the acceleration?

 

[Doc Al]

so, how would i be able to find the acceleration?

Just like you tried to do, only first find the mass of the crate. How do weight and mass relate to each other?

 

[Joe26]

Got it, thanks. W=mg...find m using weight and use f=ma to find acceleration.