A nail on a vertical with is pulled means of cord attached to it's head. If the cord make angle of 60°to the horizontal and it exert a force of 80N on the nail. find (a)The effective force which tend to pull the nail out of the wall. (b)The force which tend to bend the nail.
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To find the effective force that tends to pull the nail out of the wall, we need to use the concept of resolving forces into components.
(a) The effective force that tends to pull the nail out of the wall is the component of the force exerted by the cord that acts parallel to the wall. We can find this force using trigonometry.
The force exerted by the cord can be divided into two components: one perpendicular to the wall and one parallel to the wall. The force perpendicular to the wall does not contribute to pulling the nail out.
We can use the formula: F = F_parallel = F_cord * sin(theta), where F_cord is the force exerted by the cord (80 N) and theta is the angle between the cord and the horizontal (60 degrees).
F_parallel = 80 N * sin(60 degrees)
F_parallel ≈ 80 N * 0.866 (approximately)
F_parallel ≈ 69.28 N (approximately)
So, the effective force that tends to pull the nail out of the wall is approximately 69.28 N.
(b) To find the force that tends to bend the nail, we need to determine the component of the force exerted by the cord that acts perpendicular to the wall.
Using the same formula as above, we can find the force perpendicular to the wall:
F_perpendicular = F_cord * cos(theta)
F_perpendicular = 80 N * cos(60 degrees)
F_perpendicular ≈ 80 N * 0.5 (approximately)
F_perpendicular ≈ 40 N (approximately)
So, the force that tends to bend the nail is approximately 40 N.