Answer:
Normal force: 167.48 N
Explanation:
- First of all it is necessary to draw the free body diagram of the suitcase adding alll the forces stated on the question: the normal force, the friction force and pull force exterted by the woman. Additionally, we need to add the weight, the forces exerted by Earth's gravity. I attached the diagram so you can check it.
- We need to resolve all the unknown quantities on this exercise, so we need to write down the sum of forces equations on X-Axis and Y-axis. Remember that force exerted by the woman has an angle with respect the horizontal (X-Axis), that is to say it has force compoents on both X and Y axis. The equations will be equal to zero since the suitcase is at constant speed (acceleration is zero).
∑[tex]F_{x}[/tex]: [tex]F{x}-20 = 0[/tex]
∑[tex]F_{y}[/tex]: [tex]N -W+F_{y}=0[/tex]
- Our objetive is to find the value of the normal force. It means we can solve the sum of Y-axis for N. The solution would be following:
[tex]N = W - Fy[/tex]
- Keep in mind Weight of the suitcase (W) is equal to the suitcase mass times the acceleration caused by gravity (9.81[tex]\frac{m}{s^{2}}[/tex]. Furthermore, Fy can be replaced using trigonometry as [tex]Fsin(\theta)[/tex] where θ is the angle above the horizontal. So the formula can be written in this way:
[tex]N = mg -Fsin(\theta)[/tex]
- We need to find the value of θ so we can find the value of N. We can find it out solving the sum of forces on X-axis replacing Fx for Fcos(θ). The equation will be like this:
[tex]Fcos(\theta) -20 = 0[/tex] ⇒ [tex]Fcos(\theta) = 20[/tex][tex]\theta
[tex]\theta=cos^{-1}(20/F)[/tex]
- Replacing the value of F we will see θ has a value of 55.15°. Now we can use this angle to find the value of N. Replacing mass, the gravity acceleration and the angle by their respective values, we will have the following:
[tex]N = 20 x 9.81 - 35sin(55.15)[/tex] ⇒ [tex]N = 167.48 N[/tex]
