Question

Question: http://prnt.sc/d1j6x6
a) Write the force equations for the vertical and horizontal directions.
b) Using the equations in part (a), calculate the minimum force needed to move the crate if the force is applied at an angle of 45 degrees to the horizontal? [Answer: 28 N]

Answer 1

Free body diagram I created: http://prnt.sc/d1jabu

My attempt for ‘a)’:
Horizontally, sum of forces = 0
Therefore,
F*cos(theta) = Fr

Vertically, sum of forces = 0
Therefore,
Fn + F*sin(theta) = W

Have I done this correct so far?

b) If the equations above are correct, how can I use them to find the required force?
My guess is to rearrange and use substitution but not exactly sure about it.

Answer 2

\(F \cos(\theta) = \color{red}{\mu} F_r \)

\(F_r + F \sin(\theta) = W\)

check for yourself, not sure bout yer n and r subscripts

...I'm taking \(F_r\) as the vertical reaction at the interface so the horizontal friction term is \(\mu F_r\)

then some algebra....


\(\dfrac{F \cos(\theta)}{\mu} + F \sin(\theta) = W\)

you have the numbers to solve for F, using the static friction coefficient,

....as that is the friction that needs to be overcome before motion begins and the coefficient becomes the lower dynamic one

Answer 3

pour les autres...

Answer 4

Thank you! I got the right answer. I wasn't exactly sure how to substitute one equation into the other but after reading your answer, I understand how to do it. I appreciate you help :)

Answer 5

yesh!

have a meddle :-))