Question

A wrench 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

Answer 1

D <A <B <C

Step-by-step 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