a boy is pulling on a wagon with a force of 70 N directed at an angle of 30 degrees to the horizontal. What force is the wagon being pulled horizontally?
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since given angle is 30 deg to the horizontal, the horizontal force is just,
Fx = F*cos(theta)
Fx = 70*cos(30)
now simplify this.
34.64
X- 60.0 N
Y- 35 N
To find the horizontal component of the force being applied to the wagon, we need to determine the magnitude of the force when it is directed horizontally.
Given:
Force applied by the boy, F = 70 N
Angle between the force and the horizontal, θ = 30 degrees
We can use trigonometry to determine the horizontal component of the force. The horizontal component can be calculated using the formula:
Force_horizontal = Force × cos(θ)
Substituting the given values:
Force_horizontal = 70 N × cos(30 degrees)
Using a calculator or referring to a trigonometric table, we can find that the cosine of 30 degrees is approximately √3/2.
Simplifying:
Force_horizontal ≈ 70 N × (√3/2)
Force_horizontal ≈ 70 N × 0.866
Force_horizontal ≈ 60.62 N
Therefore, the wagon is being pulled horizontally with a force of approximately 60.62 N.