Answer: Thus, the force is directed 72.5° above the horizontal.
Explanation:
The magnitude of the force, F = 15 N
let this force be detected at angle θ from the horizontal, then horizontal component of force is: F cos θ
and vertical component is F sin θ
Horizontal component is given,
F cos θ = 4.5 N
⇒15 N cos θ = 4.5 N
⇒ cos θ = 0.3
⇒ θ = cos⁻¹ 0.3 = 72.5°
The force is directed at about 73° above the horizontal
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
Given:
F = 15 N
Fx = 4,5 N
Unknown:
θ = ?
Solution:
To solve this problem, we will use the basic principles of trigonometry.
[tex]\cos \theta = \frac{ adjacent }{ hypotenuse }[/tex]
[tex]\cos \theta = \frac{F_x}{F}[/tex]
[tex]\cos \theta = \frac{4.5}{15}[/tex]
[tex]\cos \theta = 0.3[/tex]
[tex]\theta = \cos^{-1} 0.3[/tex]
[tex]\theta \approx 73^o[/tex]
The force is directed at about 73° above the horizontal.
For more details, it can be seen in the picture attached.
Grade: High School
Subject: Physics
Chapter: Dynamics
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
