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Chapter 10: Problem 21

A \(110-\mathrm{N} \cdot \mathrm{m}\) torque is needed to start a revolving door rotating. If a child can push with a maximum force of \(90 \mathrm{N},\) how far from the door's rotation axis must she apply this force?

Short Answer

Expert verified
The child needs to apply the force approximately 1.22 meters from the door's rotation axis.

Step by step solution

01

Understanding the Problem

We are given torque (T) to start a revolving door rotating is 110 Nm. The maximum force (F) a child can apply is 90 N. We are required to find the distance from the door's rotation axis (d) where this force should be applied.
02

Apply Torque Formula

We can apply the formula for torque which is \(T = F \cdot d\).
03

Rearrange the Formula

As we are trying to find the 'd', we need to rearrange the formula to get it. The rearranged formula will be \(d = T / F\).
04

Substitute the Provided Values

Next, we substitute the values into the rearranged formula from step 3: \(d = 110 Nm/90 N\).
05

Solving for Distance

Perform the division operation to obtain the required distance. This will give us \(d \approx 1.22 m\). This is the distance from the door's rotation axis where the child's force must be applied to create the necessary torque for starting the door's rotation.

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