Summing forces: finding acceleration and F_n

[cag805]

1. Homework Statement
Use the steps outlined above to find the magnitude of the acceleration a of a chair and the magnitude of the normal force FN acting on the chair: Yusef pushes a chair of mass m = 55.0 kg across a carpeted floor with a force F⃗ p (the subscript 'p' here is lowercase and throughout the question) of magnitude Fp = 160 N directed at θ = 35.0 degrees below the horizontal (Figure 1) . The magnitude of the kinetic frictional force between the carpet and the chair is Fk = 107N .

What is the magnitude of the acceleration a of the chair? What is the magnitude of the normal force FN acting on the chair?
Express your answers, separated by a comma, in meters per second squared and Newtons to three significant figures.

Homework Equations

ΣFx = Fpcosθ−Fk = m * a_x
ΣFy = FN−FG−Fpsinθ =m * a_y

The Attempt at a Solution

a_x

a

F_n

Answers

 

[Doc Al]

Redo your calculation of the normal force. The applied force acts downward and thus must increase the normal force.

 

[cag805]

Ah that makes sense. However, in F_N = F_g + F_py, F_py = 160N * sin(325) which gives me a negative number. The problem states that the force is applied at -35 degrees. Intuitively,I now know that greater pushing force increases normal force... but what can I do when I'm given an angle like this? Maybe add 180 degrees?

 

[Doc Al]

Ah that makes sense. However, in F_N = F_g + F_py, F_py = 160N * sin(325) which gives me a negative number. The problem states that the force is applied at -35 degrees. Intuitively,I now know that greater pushing force increases normal force... but what can I do when I'm given an angle like this? Maybe add 180 degrees?

Don't just plug in numbers blindly. What does the minus sign mean? Just that it points downward. So be consistent. If F_py is negative, so should F_g be negative. They both point down.

 

[cag805]

But leaving it as negative gives me the incorrect answer?

F_N = F_g + F_py = 539N + 160 * sin(325)
F_N = 539N - 91.77N = ~447N (incorrect)

F_N = F_g + F_py = 539N + 160 * sin(325 + 180)
F_N = 539N + 91.77N = ~631N(correct)

 

[Doc Al]

But leaving it as negative gives me the incorrect answer?

You must be consistent. If that force is negative, so must be F_g. And the equation you want is ΣF_y = 0.