Awrench is used to loosen a tight bolt. rank the configurations in order of the applied torque, from least to most. in a only the wrench is used. in b, an extender bar is used, perpendicular to the wrench. in c the extender is used parallel to the wrench. in d the force is not perpendicular to the wrench. the applied force is the same in each case.

(a) d, a=b, c
(b) a, b, d, c
(c) d, a, b, c
(d) a=b=c=d

D <A <B <C

Explanation:

When the wrench is used to loosen a bolt, torque is being applied to the system. The torque is defined by

        τ = F x r

Where F is the force and r the distance from the force applied point to the pivot point

       τ = F r sin θ

In this case the angle is between force and distance.

Let's look at the characteristics of this equation.

The torque is maximum if at an angle it is 90 °     τ = F r

Let's analyze the affirmations

A gives a torque that you will call τ₀  = F r

B the troque increases because the distance increases the new distance we can find it by the Pythagorean Theorem

      R ’= √r² + d² = r √ (1+ d² / r²)

      τ = τ₀  (1+ (d /r)²)

C the torque increases because the distance increases

       R ’= r + d

       τ = τ₀ (1 + d/r)

D the force is not perpendicular to the key in this case the sine decreases and therefore the torque decreases

       τ = F r sin θ

       τ = τ₀ sin θ

order   Minor   to   major

D <A <B <C

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