An elephant drags a tree trunk along a rough horizontal surface by means of an attached rope which makes an angle of 30° with the horizontal. The force in the rope is 4 000N. CALCULATE the horizontal component of the force exerted by the rope on the tree trunk
What is 4000N*cos30deg?
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To calculate the horizontal component of the force exerted by the rope on the tree trunk, we can use trigonometric functions. The horizontal component of the force can be determined by finding the cosine of the angle between the rope and the horizontal surface.
We are given:
Force in the rope (T) = 4,000 N
Angle (θ) = 30°
Let's calculate the horizontal component of the force:
Horizontal Component of Force (Fh) = Force in the rope (T) * cos(θ)
Substituting the given values:
Fh = 4,000 N * cos(30°)
Using the cosine of 30°:
Fh ≈ 4,000 N * 0.866
Calculating the value:
Fh ≈ 3,464 N
Therefore, the approximate horizontal component of the force exerted by the rope on the tree trunk is 3,464 N.
To calculate the horizontal component of the force exerted by the rope on the tree trunk, we need to find the cosine of the angle between the rope and the horizontal surface. Let's denote this horizontal force component as Fx.
We know that the force in the rope is 4,000N, and the angle between the rope and the horizontal is 30°. Using trigonometry, we can find the horizontal component as follows:
Fx = Force in the rope * cosine(angle)
Substituting the given values:
Fx = 4,000N * cos(30°)
To calculate the cosine of 30°, we can use a scientific calculator or reference table. The cosine of 30° is approximately 0.866.
Fx = 4,000N * 0.866
Fx = 3,464N
Therefore, the horizontal component of the force exerted by the rope on the tree trunk is approximately 3,464N.