Question

) a wrench 0.6 meters long lies along the positive y-axis, and grips a bolt at the origin. a force is applied in the direction of ⟨0,1,3⟩ at the end of the wrench. find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt.

Answer 1

The magnitude of the force needed to supply 100 newton-meters of torque to the bolt is approximately 166.67 N.

Step-by-step explanation:

To find the magnitude of the force needed to supply 100 newton-meters of torque to the bolt, we can use the formula for torque, which is the product of the force and the distance from the point of rotation.

In this case, the force applied is in the direction of ⟨0,1,3⟩ and the length of the wrench is 0.6 meters. We need to find the magnitude of the force, so we can use the equation torque = force x distance.

Given torque = 100 N·m and distance = 0.6 m, we can rearrange the equation to solve for force: force = torque / distance.

Substituting the values, we have force = 100 N·m / 0.6 m = 166.67 N.

Therefore, the magnitude of the force needed to supply 100 newton-meters of torque to the bolt is approximately 166.67 N.

Answer 2

Applied Force Direction vector = [0,1,3] force F = j + 4k torque is t = 100 Newton-meters = r x F Wrench is 0.5 meters long on positive side of the y-axis, r = 0.6 = [0,0.6,0] We know torque |t| = |r x F| = |r| x |F| sin theta r x F = |r| x |F| cos theta r x (j + 3k) = |r| x |j + 3k| cos theta => [0,0.6,0] [0,1,3] = 0.6 x squareroot of ((0)^2 + (1)^2 + (3)^2) cos theta => 0.6 = 0.6 x squareroot of (1 + 9) cos theta => cos theta = 1 / squareroot of (10) Calculationg the sin theta, sin theta = squareroot of (1 - (1 / squareroot of (10))^2) = squareroot of (9/10) sin theta = 3 / squareroot of (10) Substituting the values, |T| = |r| x |F| sin theta => 100 = |0.6| x |F| x 3 / squareroot of (10) |F| = (100 x squareroot of (10)) / 1.8 |F| = (1000 / 18) x squareroot of (10) Magnitude of force |F| = 55.55 x squareroot of (10)