Question

A wrench 0.5 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of <0,1,4> 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

Length of the wrench is 0.5 m.

Since the wrench lies along the axis, .

A force is applied in the direction of .

Magnitude of the torque is  N-m.

Torque is defined as the cross product of position and force vectors.

Magnitude of the torque  .

Find the dot product to estimate the angle between them.

Find .

.

Magnitude of the torque  .

Substitute corresponding values in the expression.

Magnitude of the force is  N.