Respuesta :
Answer:
(a). The resultant of these forces is 1216.55 N.
(b). The direction of the resultant forces is 80.53°.
Explanation:
Given that,
First force = 1200 N
Second force = 200 N
(a). We need to calculate the resultant of these forces
Using cosine law
[tex]F=\sqrt{F_{1}^2+F_{2}^2+2F_{1}F_{2}\cos\theta}[/tex]
Put the value into the formula
[tex]F=\sqrt{1200^2+200^2+2\times1200\times200\cos90}[/tex]
[tex]F=\sqrt{1200^2+200^2}[/tex]
[tex]F= 1216.55\ N[/tex]
The resultant of these forces is 1216.55 N.
(b). We need to calculate the direction of the resultant forces
Using formula of direction
[tex]\tan\alpha=\dfrac{F_{1}}{F_{2}}[/tex]
Put the value into the formula
[tex]\alpha=\tan^{-1}(\dfrac{1200}{200})[/tex]
[tex]\alpha=80.53^{\circ}[/tex]
Hence, (a). The resultant of these forces is 1216.55 N.
(b). The direction of the resultant forces is 80.53°.
Answer:
a) [tex]F_r=1216.55\ N[/tex]
b) [tex]\theta=80.54^{\circ}[/tex]
Explanation:
Given:
- force acting upward on the, [tex]F_y=1200\ N[/tex]
- force acting forward on daisy, [tex]F_x=200\ N[/tex]
a)
Now the resultant of these forces:
Since the forces are mutually perpendicular,
[tex]F_r=\sqrt{F_x^2+F_y^2}[/tex]
[tex]F_r=\sqrt{200^2+1200^2}[/tex]
[tex]F_r=1216.55\ N[/tex]
b)
The direction of this force from the positive x-direction:
[tex]\tan\theta=\frac{F_y}{F_x}[/tex]
[tex]\tan\theta=\frac{1200}{200}[/tex]
[tex]\theta=80.54^{\circ}[/tex]
