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# A crate of mass m = 100kg is pushed at constant speed up a frictionless ramp $\theta=30^{\large\circ}$ by a horizontal force $\overrightarrow{F}$.What are the magnitudes of $\overrightarrow{F}$ and the force of the crate from the ramp?

$\begin{array}{1 1}556N,F_N=1.13\times 10^3N\\278N,F_N=1.13\times 10^4N\\446N,F_N=1.13\times 10^3N\\556N,F_N=1.13\times 10^4N\end{array}$

Answer : $556N,F_N=1.13\times 10^3N$
Free body diagram :
We resolve this horizontal force into appropriate components
Newton's second law applied to the x-axis produces
$F\cos\theta-mg\sin\theta=ma$
For $a=0$,this yields $F=566$N
Applying Newton's second law to the y axis (where there is no acceleration),we have
$F_N-F\sin \theta-mg\cos \theta = 0$
Which yields the normal force $F_N=1.13\times 10^3N$