Question

A wrench 20 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction 0, 4, −3 at the end of the wrench. Find the magnitude of the force needed to supply 150 N · m of torque to the bolt. (Round your answer to the nearest whole number)

Answer 1

Answer:

1250 N

Explanation:

length of wrench = 20 cm = 0.2 m

Write the length of wrench in vector form

r = 0.2 j metre

Direction of force= $\frac{0i+4j-3k}{\sqrt{0 + 16 + 9}}=\frac{0i+4j-3k}{5}$

Let the magnitude of force is F

So, write the force in vector form

F = F  $\frac{0i+4j-3k}{\sqrt{0 + 16 + 9}}=\frac{0i+4j-3k}{5}$

torque, T = 150 Nm

Torque = T = r x F

$150 i =0.2j\times F\frac{0i+4j-3k}{5}$

F = 1250 N

Thus, the magnitude of force is 1250 N.