Given
F = 1.1x10^3 N
u = 0.13
m = 517 kg
a = 0.67 m/s^2 (?)
Procedure
B: Physics representation
Free body diagram
C: Word representation
The figure above is the free body diagram for the problem stated. As can be seen, the interacting forces are weight, normal, friction, and cable tension.
Let's make use of Newton's second law. For this, we will make the summation of forces on the x-axis and on the y-axis.
D: Mathematical representation
Step 1: 2nd Newton law
Equation 1: x-axis summation
[tex]T\sin 37-\mu_kN=ma[/tex]
Equation 2: y-axis summation
[tex]\begin{gathered} T\cos 37+N-mg=0 \\ \end{gathered}[/tex]
Step 2: Replacing variables
From the summation of forces in y-axis we will clear the normal and then we will replace it in the summation of forces in x-axis
Equation 3: Normal force
[tex]N=mg-T\cos 37[/tex][tex]\begin{gathered} T\sin 37-\mu_k(mg-T\cos 37)=ma \\ a=\frac{T\sin37-\mu_k(mg-T\cos37)}{m} \\ a=\frac{1100\cdot\sin37-0.13(517\operatorname{kg}\cdot9.8m/s^2-1100\cdot\cos37)}{517\operatorname{kg}} \\ a=0.227m/s^2 \\ \text{Equation 4 : Acceleration } \\ \end{gathered}[/tex]
Step 3: Solution
Solution
The calculated acceleration for the cart will be 0.227 m/s^2.
Therefore, the force will produce an acceptable acceleration.
