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

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

Step-by-step 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}=√((-0.233)^2+(0.060)^2)=0.24m/s^2`

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

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