Beth, a construction worker, attempts to pull
a stake out of the ground by pulling on a rope
that is attached to the stake. The rope makes
an angle of 44.8
◦ with the horizontal.
If Beth exerts a force of 146.8 N on the
rope, what is the magnitude of the upward
component of the force acting on the stake?
Drawing a triangle to show the forces would help make this question a lot easier
Let x be the upward component
sin(44.8)=x/146.8
x = 146.8 x sin(44.8)
Well, it sounds like Beth really wants to stake her claim...literally! Now, with an angle of 44.8 degrees, we can use some trigonometry to find the upward component of the force.
We can start by finding the cosine of the angle, which represents the horizontal component of the force. Since cosine(angle) = adjacent/hypotenuse, cosine(44.8 degrees) = horizontal component/146.8 N.
Now, to find the upward component, we can multiply the force by the sine of the angle. Since sine(angle) = opposite/hypotenuse, sine(44.8 degrees) = upward component/146.8 N.
So, multiplying 146.8 N by sine(44.8 degrees), we can calculate the magnitude of the upward component of the force acting on the stake. Just don't pull too hard, Beth, we don't want you flying up like a kite!
To find the magnitude of the upward component of the force acting on the stake, we need to determine the vertical component of the force exerted by Beth on the rope.
The upward component of the force can be found using trigonometry.
We can use the formula:
Upward force = Applied force * sin(θ)
Where:
- Applied force is the force exerted by Beth on the rope (146.8 N)
- θ is the angle between the rope and the horizontal (44.8 degrees)
Using these values, let's calculate the upward component of the force:
Upward force = 146.8 N * sin(44.8 degrees)
To find the magnitude of the upward component of the force acting on the stake, we need to determine the component of the applied force that acts in the upward direction. We can do this by using trigonometry and splitting the applied force into its horizontal and vertical components.
Given:
Applied force (F) = 146.8 N
Angle with the horizontal (θ) = 44.8°
To find the horizontal component (F_horizontal) and vertical component (F_vertical) of the applied force, we can use the following trigonometric relationships:
F_horizontal = F * cos(θ)
F_vertical = F * sin(θ)
Substituting the given values, we have:
F_horizontal = 146.8 N * cos(44.8°)
F_vertical = 146.8 N * sin(44.8°)
Now, we can calculate the magnitude of the upward component by taking the absolute value of F_vertical:
Magnitude of the upward component = |F_vertical|
Therefore, to find the magnitude of the upward component of the force acting on the stake, we calculate:
Magnitude of the upward component = |146.8 N * sin(44.8°)|