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8. While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and
she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis.
Determine the magnitude of the torque about her elbow.
(Show work)

54.8 Nm

Step-by-step explanation:

Torque is the cross product of the radius vector and force vector:

τ = r × F

Another way to write it is the product of the radius and force magnitudes times the sine of the angle between the vectors.

τ = rF sin θ

Here, r = 0.366 meters and F = 155 Newtons.  F is in the +y direction, and r is 15° below the +x axis, so the angle between the vectors is 90° − 15° = 75°.

τ = (0.366 m) (155 N) (sin 75°)

τ = 54.8 Nm

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