Solving Frictionless Horizontal Motion: Find Block's Speed

[jti3066]

Homework Statement

A 5.86 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a force F = 10.00 N at an angle = 35.0° above the horizontal (x-axis). What is the speed of the block 3.70 seconds after it starts moving?

Homework Equations

Fcos() - ma = 0

Fsin() - mg = 0

V_f = V_0 + at (V_0 = 0)

The Attempt at a Solution

Since the first two equations are equal to zero I set them equal to each other and then solved for acceleration. I then used this in the last equation to solve for V_f. Apparently I am doing something wrong because I am not getting the correct answer.

 

[rl.bhat]

What is the value of the acceleration? Will you show your calculations?

 

[jti3066]

Fcos() - ma = 0

Fsin() - mg = 0

so setting these two equations together and inputting given data:

10cos(35) - 5.86(a) = 10sin(35) -5.86(9.81)

8.192 - 5.86(a) = 5.736 - 57.487

-5.86(a) = 5.736 - 57.487 - 8.192

-5.86(a) = -59.943

a = 10.22918089 m/s^2

Now to solve for V_f (final velocity)

V_f = V_0 + at

V_f = 0 + 10.23(3.7) = 37.84 m/s

FAIL! This is the wrong answer

 

[rl.bhat]

10cos(35) - 5.86(a) = 10sin(35) -5.86(9.81)

This step is wrong. There is no acceleration in the vertical direction because the action and reaction are equal and opposite. Hence

F*cos(θ) = ma

 

[jti3066]

Ok...got it

This always holds true correct, except when the object is inclined/declined

here are the proper calculations:

10cos(35) = 5.86(a)

a = 1.39 m/s^2

V_f = 0 + 1.39(3.7) = 5.17 m/s

correct answer

Thanks a bunch