Part A: Suppose the direction of the force changes from a 48° angle with the
floor to a 70° angle with the floor. Determine the effect on the horizontal and
vertical components of the force. Give forces to the nearest hundredth of a
unit

Respuesta :

Answer:

Horizontal Component of Force decreases and Vertical Component Increases.

Step-by-step explanation:

The rectangular components of a Force are given by:

Horizontal Component:

[tex]F_{x}=Fcos(\theta)[/tex]

Vertical Component:

[tex]F_{y}=Fsin(\theta)[/tex]

Here, F represents the magnitude of the Force and Θ is the angle between the Force F and the horizontal.

The initial value of Θ is 48 degrees. So under this condition the rectangular components will be:

[tex]F_{x}=Fcos(48)=0.67F\\\\ F_{y}=Fsin(48)=0.74F[/tex]

On increasing the angle to 70 degrees, the new rectangular components will be:

[tex]F_{x}=Fcos(70)=0.34F\\\\ F_{y}=Fsin(70)=0.94F[/tex]

From the above calculations we can see that on increasing the angle made by the Force with floor from 48 degrees to 70 degrees:

  • Horizontal component decreases from 0.67F to 0.34F
  • Vertical component increases from 0.74F to 0.94F

If the value of Force F is known, the exact value of rectangular components can be calculated from the previous expressions.