Question

A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle θ above the horizontal. She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. What is the magnitude of the normal force that the ground exerts on the suitcase?

Answer 1

Normal force: 167.48 N

Step-by-step 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).

∑
`F_(x)`:
`F{x}-20 = 0`

∑
`F_(y)`:
`N -W+F_(y)=0`

• 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:

`N = W - Fy`

• Keep in mind Weight of the suitcase (W) is equal to the suitcase mass times the acceleration caused by gravity (9.81
  `(m)/(s^(2))`. Furthermore, Fy can be replaced using trigonometry as
  `Fsin(\theta)` where θ is the angle above the horizontal. So the formula can be written in this way:

`N = mg -Fsin(\theta)`

• 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:

`Fcos(\theta) -20 = 0` ⇒
`Fcos(\theta) = 20`
`\theta                   </p><p>         [tex]\theta=cos^(-1)(20/F)`

• 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:

`N = 20 x 9.81 - 35sin(55.15)` ⇒
`N = 167.48 N`