A crowbar is used to pull a nail. The length of the effort arm of the crowbar is 26 cm and the resistance arm is 4.2 cm. What force in N is required to pull a nail if the friction force holding the nail in place is 120 N?
To determine the force required to pull the nail using a crowbar, we can use the principle of moments. The principle of moments states that the sum of the moments acting on an object is equal to zero when the object is in equilibrium.
In this case, the clockwise moment due to the friction force holding the nail in place is balanced by the counterclockwise moment generated by the force applied on the effort arm of the crowbar.
The moment of a force is calculated by multiplying its magnitude by the distance from the point of rotation (fulcrum) to the line of action of the force.
Let's assign variables to the unknowns:
- Length of the effort arm (EA) = 26 cm = 0.26 m
- Length of the resistance arm (RA) = 4.2 cm = 0.042 m
- Friction force (Ff) = 120 N
- Force required to pull the nail (F) = ?
Now, using the principle of moments, we can set up the equation:
Ff × RA = F × EA
Substituting the values:
120 N × 0.042 m = F × 0.26 m
Simplifying the equation:
5.04 Nm = 0.26 F
We can now solve for F:
F = 5.04 Nm / 0.26 m
Calculating the value:
F ≈ 19.38 N
Therefore, a force of approximately 19.38 N is required to pull the nail using the crowbar.