a foolish boy remove a nail from a vertical wall by pulling a stick attached to the nail in a direction 30 deg to the wall.
if the tension in the stick is 10cm , calculate the magnitude of the force wich is not effective in pulling out the nail, is it possible to remove the nali thos way if minimum force required is 7N?
why is the boy foolish?
Is it correct
To calculate the magnitude of the force that is not effective in pulling out the nail, we need to determine the component of the tension force that acts in the direction perpendicular to the wall. This force is what causes the nail to come out.
Given:
Angle between the stick and the wall (θ) = 30 degrees
Tension in the stick (T) = 10 N
Now, let's calculate the perpendicular component of the tension force:
Perpendicular component (T_perpendicular) = T * sin(θ)
= 10 N * sin(30 degrees)
≈ 5 N
Therefore, the magnitude of the force that is not effective in pulling out the nail is approximately 5 N.
Now, if the minimum force required to pull out the nail is 7 N, it is not possible for the boy to remove the nail using the given force of 10 N. The force applied by the boy is not sufficient to overcome the resistance provided by the nail.
The boy is considered foolish because he is using a force that is less than the minimum force required to pull out the nail. It is important to apply a force greater than or equal to the minimum force required to successfully accomplish the task.
To determine the magnitude of the force that is not effective in pulling out the nail, you will need to calculate the vertical component of the force applied by the stick.
First, let's draw a diagram to visualize the situation.
```
|\
| \
| \ <-- Wall
| \
| \
| \
--------
| <-- Nail
|
Stick pulled at 30 degrees to the wall
```
We can see from the diagram that the force applied by the stick can be divided into two components: one horizontal (parallel to the wall) and one vertical (perpendicular to the wall). The vertical component is the one that affects the nail.
To calculate the vertical component, we use trigonometry. Since the stick is pulled at a 30-degree angle, the vertical component can be found using the sine function:
sin(30 degrees) = vertical component / tension in the stick
Recall that the tension in the stick is given as 10 N. So, rearranging the equation:
vertical component = sin(30 degrees) * tension in the stick
vertical component = sin(30 degrees) * 10 N
Using a calculator, we find that sin(30 degrees) is equal to 0.5:
vertical component = 0.5 * 10 N
vertical component = 5 N
Therefore, the magnitude of the force that is not effective in pulling out the nail is 5 N.
Now, let's determine if it is possible to remove the nail this way. The boy foolishly attempts to remove the nail by pulling with a force magnitude of 10 N (tension in the stick). However, the minimum force required to pull out the nail is stated as 7 N.
Since the vertical component of the force is only 5 N, which is less than the minimum required force of 7 N, it is not possible to remove the nail using this method. The force applied by pulling the stick at a 30-degree angle is not sufficient to overcome the resistance of the nail.
Therefore, the boy is considered foolish because he is using a method that does not provide enough force to accomplish the task.
a. Tension = 10 N.
Fx = 10*Cos30 =
b. Fy = 10*sin30 = 5 N. = vertical component of force.
7 N is required.