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 60.9
◦
with the horizontal.
If Beth exerts a force of 116 N on the rope,
what is the magnitude of the upward component of the force acting on the stake?
Answer in units of N
F(y) =Fsinα
108n
To find the magnitude of the upward component of the force acting on the stake, we need to calculate the vertical or upward component of the force. Here's how we can do that:
1. Draw a diagram: Begin by drawing a right triangle to represent the situation. Label one side as the horizontal direction (adjacent side), one side as the vertical direction (opposite side), and the hypotenuse as the force applied on the rope.
|
- | -
|
^ |
- |
60.9°
|_______>
2. Identify the given values: From the problem statement, we know that the rope makes an angle of 60.9 degrees with the horizontal (adjacent side) and that the force exerted by Beth on the rope is 116 N.
3. Find the vertical component: To find the vertical component of the force, we use the formula:
Vertical component = Force × sin(angle)
Substituting the given values:
Vertical component = 116 N × sin(60.9°)
4. Calculate the magnitude: Use a calculator to solve the equation:
Vertical component = 116 N × 0.8742
= 101.286 N
Therefore, the magnitude of the upward component of the force acting on the stake is approximately 101.286 N.