A body pulls a nail from the wall with a string tied to a nail. The string is inclined at an angle of 60° to the wall. If the tension in the string is 4N,what is the effective force used in pulling the nail?
To find the effective force used in pulling the nail, we need to find the component of the tension in the string that is parallel to the wall.
Since the angle between the string and the wall is 60°, the component of the tension in the string that is parallel to the wall can be found using the formula:
F_parallel = Tension * cos(angle)
where:
- F_parallel is the component of tension parallel to the wall
- Tension is the tension in the string
- angle is the angle between the string and the wall
Plugging in the given values, we have:
F_parallel = 4N * cos(60°)
F_parallel = 4N * 0.5
F_parallel = 2N
Therefore, the effective force used in pulling the nail is 2N.
To find the effective force used in pulling the nail, we need to resolve the tension force into its horizontal and vertical components.
Given:
Tension in the string (T) = 4 N
Angle of inclination (θ) = 60°
First, let's find the vertical component of the tension force (Tv).
Tv = T * sin(θ)
Tv = 4 N * sin(60°)
Tv = 4 N * 0.866 (rounded to 3 decimal places)
Tv ≈ 3.464 N
Now, let's find the horizontal component of the tension force (Th).
Th = T * cos(θ)
Th = 4 N * cos(60°)
Th = 4 N * 0.5
Th = 2 N
The effective force used in pulling the nail is the horizontal component (Th) of the tension force.
Therefore, the effective force used in pulling the nail is 2 N.