Question

The 20-N horizontal force acts on the handle of the socket wrench. Determine the moment of this force about point O. Specify the coordinate direction angles α,β,γ of the moment axis.

Answer 1

The torque applied to a nut with a force at an angle can be calculated using the formula T = F * R * sin(θ), where F is the force, R is the distance from the pivot, and θ is the angle. The maximum torque occurs when the force is applied perpendicular to the lever arm (90° angle).

Step-by-step explanation:

The magnitude and direction of a torque depend on the force applied and the distance from the pivot point, along with the sine of the angle between the force and the lever arm. For the initial case, the torque (T) applied by a 20.00-N force at a 40° angle and at 0.25 m from the nut can be calculated using the formula T = F * R * sin(θ), where F is the force, R is the distance (radius), and θ is the angle in question. For angle y = 40°, θ is equivalent to y, and the torque would be T = 20 N * 0.25 m * sin(40°).

When calculating torque for a different angle p = 45°, we simply adjust the angle in the equation accordingly: T = 20 N * 0.25 m * sin(45°). The torque has the largest magnitude when the force is applied perpendicular to the wrench handle, which occurs at an angle of 90° (sin(90°) = 1). Hence the maximum torque would be Tbest = 20 N * 0.25 m = 5.00 N⋅m.

Answer 2

The moment of the force about point B is -4000 Nm, and the direction angles of the moment axis are α = 0°, β = 90°, and γ = 0°.

Combine exponents: We can simplify the expression by combining the exponents of the various terms.

Solve for the moment: Once we have a simplified expression, we can solve for the moment of the force about point B.

Find the direction angles: Finally, we can use the cross product to find the direction angles α, β, and γ of the moment axis.

Steps to solve:

Combine exponents:

`M_B=20 \mathrm{~N} \cdot(-200 \mathrm{~mm}) \sin \left(90^(\circ)\right)=-4000 \mathrm{Nm}`

Solve for the moment:

`M_B=-4000 N m`

Find the direction angles:

The direction angles of the moment axis are α = 0°, β = 90°, and γ = 0°.