Question
please solve the last part
theta
A wrench 35 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction 0, 3, -4 at the end of the wrench. Find the magnitude of the force needed to supply 60 N middot m of torque to the bolt. The magnitude of the torque tau developed by applying a force F at a point with position vector r at an angle theta to r is given by |tau| = |r times F|. In terms of theta and the vector magnitudes, this can be expressed as |tau| = |r| |F| We have |tau| = 60 N middot m. We also have r = 0, 0.35, 0 and so |r| = meters. In order to find |F|, we will have to find the angle theta between F and r. We can use the equation Using the equation above, we see that the angle is as follows. (Round your answer to one decimal place.)
Explanation / Answer
theta = cos^-1{ <0 ,0.35 ,0> . <0 ,3 , -4 > / ( 0.35 * sqrt(25) ) }
= cos^-1 ( 3/5 )
= 53 . 1 degree
