Question

wo ropes are attached to a 40kg object. The rope with a 50N force points along a direction 49 degrees from the positive x-axis, and the other robe with a 55N force points along a direction 220 degrees. What is the acceleration of the object?

Answer 1

Answer:

     Acceleration is 0.24 m/s² at 104.44° to positive x-axis.

Explanation:

Refer the figure given.

Let us take component i along positive X axis and component j along positive Y axis.

50 N force can be resolved in to 50 cos 49 i + 50 sin 49 j

        F1 = 32.80 i + 37.74 j

55 N force can be resolved in to 55 cos 220 i + 55 sin 220 j

        F2 = -42.13 i -35.35 j

Total force

       F = F1 + F2 = 32.80 i + 37.74 j -42.13 i -35.35 j = -9.33 i + 2.39 j

We have

      F = ma = 40a =-9.33 i + 2.39 j

Acceleration

      a =-0.233 i + 0.060 j

      $\texttt{Magnitude}=\sqrt{(-0.233)^2+(0.060)^2}=0.24m/s^2$

      $\texttt{Direction},\theta =tan^{-1}\left ( \frac{0.060}{-0.233} \right )=104.44^0$

     Acceleration is 0.24 m/s² at 104.44° to positive x-axis.