Final answer:
The force F_applied to the round rod by each jaw of the pliers can be calculated using trigonometry and the given force. The force supported by the pin at A can be determined using the principle of equilibrium.
Step-by-step explanation:
For an 80-N force on the handles of the pliers, the force Fapplied to the round rod by each jaw can be found by resolving the force into its components. Since the force is applied at an angle to the rod, we can use trigonometry to find the components. Let's assume the angle between the force and the rod is θ.
The force Fapplied to the round rod by each jaw can be calculated using the formula:
Fapplied = Fcos(θ)
Substituting the given values:
Fapplied = 80 Ncos(θ
To find the force supported by the pin at A, we can use the principle of equilibrium. Since the pliers are in equilibrium, the sum of the forces acting on it must be zer
Sum of forces in the vertical direction = 0
F - 2Fapplied = 0
Simplifying the equation:
2Fapplied =
2(80 Ncos(θ)) = 80 N
160 Ncos(θ) = 80 N
cos(θ) = 0.5
θ = arccos(0.5)
Using a calculator, we can find:
θ ≈ 60°
Substiuting the value of θ into the formula for Fapplied:
Fapplied = 80 Ncos(60°
Fapplied ≈ 40 N
The force Fapplied to the round rod by each jaw is approximately 40 N, and the force supported by the pin at A is approximately 80 N.