A uniform 50-kg crate rest on a horizontal surface for which coefficient of kinetic friction is 0.2. Determine the crate acceleration if a force of P=600 N is applied to the crate as shown in figure.

enter image description here

Subject : Kinematics of Machines

Topic : Kinematics and Kinetics of rigid body

Difficulty : Medium

1 Answer

Solution :

Given :

Mass of crat $m=50~kg$


enter image description here

Applying the equation of 2nd law of motion

Along Y-axis

$\begin {aligned}\Sigma F_y &=m\left(a_{G}\right)_{y} \\ N-W &=0 .....(i) \end{aligned}$

Along X-axis

$\begin{aligned}\Sigma F_{x} &=m \left(a _{G}\right)_{x} \\ P-F &=50a_G\\ 600-0.2 N &=50 a_{G} .....(ii)\end{aligned}$

Moment at G

$\begin {aligned}\Sigma M_{G} &=0 \\ P(0.3)+N-\mu NĂ—(0.5) &=0\\ 600(0.3)+N-0.2 N(0.5) &=0\end{aligned}$

$\therefore N=490.5{~N}$ Putting in question (ii), we get

The crat acceleration is $a_{G}=10{~m}/{s}^ {2}$

Please log in to add an answer.