Solving Frictionless Horizontal Motion: Find Block's Speed

AI Thread Summary
A 5.86 kg block on a frictionless horizontal floor is pulled by a 10.00 N force at a 35° angle. The initial attempt to calculate the block's acceleration and final speed resulted in an incorrect answer due to misapplication of forces. The correct approach reveals that the vertical acceleration is zero, leading to the proper calculation of horizontal acceleration as 1.39 m/s². Consequently, the final speed of the block after 3.70 seconds is determined to be 5.17 m/s. This highlights the importance of correctly analyzing forces in physics problems.
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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.
 
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What is the value of the acceleration? Will you show your calculations?
 


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
 
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
 
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
 
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