The Brakes on a Bicycle Are Applied by Using a Downward

Multiple Choice

The brakes on a bicycle are applied by using a downward force of p pounds on the pedal when the six-inch crank makes a angle with the horizontal.Vectors representing the position of the crank and the force are $$\mathbf { V } = \frac { 1 } { 6 } \left( - \cos 70 ^ { \circ } \mathbf { j } - \sin 70 ^ { \circ } \mathbf { k } \right)$$ and $$\mathbf { F } = - p \mathbf { k }$$ respectively.The magnitude of the torque on the crank is given by $$\| \mathbf { V } \times \mathbf { F } \|$$ .Using the given information,write the torque T on the crank as a function of p.

A) $T = - \frac { p } { 5 } \sin 70 ^ { \circ }$
B) $T = \frac { p } { 3 } \cos 70 ^ { \circ }$
C) $T = - \frac { p } { 5 } \cos 70 ^ { \circ }$
D) $T = \frac { 1 } { 5 } \cos 70 ^ { \circ }$
E) $T = \frac { p } { 5 } \sin 70 ^ { \circ }$