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qwelly [4]
3 years ago
10

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?

Physics
1 answer:
Elza [17]3 years ago
7 0

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).

        ∑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\frac{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 <em>Fx</em> for Fcos(θ). The equation will be like this:

        Fcos(\theta) -20 = 0   ⇒   Fcos(\theta) = 20\theta                            [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

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