Final answer:
The torque of the couple exerted on the beam is calculated using the formula τ = F × d × sin(θ), and with a force of 8.0 N, a beam length of 0.60 m, and an angle of 60°, the torque is approximately 4.16 N·m.
Step-by-step explanation:
The question requires the calculation of the torque of a couple exerted on a beam. Torque (τ) is given by the formula τ = rF sin(θ), where r is the distance to the pivot point, F is the force applied, and θ is the angle between the force and the direction of r. For a couple, r is the length of the beam and the forces are equal and opposite. Given that the two 8.0 N forces are separated by 0.60 m and the angle θ is 60°, the torque is calculated by multiplying one of the forces with the beam length and the sine of the angle between the force and the beam.
To calculate the torque of the couple acting on the beam, the formula simplifies to: τ = F × d × sin(θ), where d = 0.60 m is the separation distance between the forces (equal to the length of the beam), F = 8.0 N is the magnitude of one of the forces, and θ = 60°. Therefore, the torque is:
τ = 8.0 N × 0.60 m × sin(60°)
Using the sine of 60°, which is √3/2 or approximately 0.866, we get:
τ = 8.0 N × 0.60 m × 0.866 ≈ 4.16 N·m
The torque of the couple exerted on the beam is approximately 4.16 N·m.