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(a) A person opens a 1.30 m wide door by pushing on it with a force of 34.5 N applied at the center of the door, at an angle perpendicular to the door's surface. magnitude of torque (in N. m) is applied about an axis through the hinges? N.m (b) A second person opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the doo magnitude of torque (in N. m) is applied about the axis through the hinges now? N. m

(a) A person opens a 1.30 m wide door by pushing on it with a force of 34.5 N applied at the center of the door, at an angle perpendicular to the door's surface. magnitude of torque (in N. m) is applied about an axis through the hinges? N.m (b) A second person opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the doo magnitude of torque (in N. m) is applied about the axis through the hinges now? N. m

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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### Torque Problems Involving Door Mechanics #### Scenario: **(a)** A person opens a 1.30 m wide door by pushing on it with a force of 34.5 N applied at the center of the door, at an angle perpendicular to the door's surface. What magnitude of torque (in N · m) is applied about an axis through the hinges? - **[Blank box for answer]** N · m **(b)** A second person opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the door. What magnitude of torque (in N · m) is applied about the axis through the hinges now? - **[Blank box for answer]** N · m #### Explanation: - **Torque Calculation:** Torque (\(\tau\)) is calculated using the formula \(\tau = r \times F \times \sin(\theta)\), where: - \(r\) is the distance from the pivot point (hinges) to the point of force application. - \(F\) is the force applied. - \(\theta\) is the angle between the force vector and the lever arm (90° in these scenarios). - **Diagram Analysis:** - Part (a) involves calculating torque when force is applied at the center of the door. - Part (b) involves calculating torque when force is applied at the edge of the door. Both scenarios emphasize understanding how the point of force application affects the torque on the door.
Transcribed Image Text:### Torque Problems Involving Door Mechanics #### Scenario: **(a)** A person opens a 1.30 m wide door by pushing on it with a force of 34.5 N applied at the center of the door, at an angle perpendicular to the door's surface. What magnitude of torque (in N · m) is applied about an axis through the hinges? - **[Blank box for answer]** N · m **(b)** A second person opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the door. What magnitude of torque (in N · m) is applied about the axis through the hinges now? - **[Blank box for answer]** N · m #### Explanation: - **Torque Calculation:** Torque (\(\tau\)) is calculated using the formula \(\tau = r \times F \times \sin(\theta)\), where: - \(r\) is the distance from the pivot point (hinges) to the point of force application. - \(F\) is the force applied. - \(\theta\) is the angle between the force vector and the lever arm (90° in these scenarios). - **Diagram Analysis:** - Part (a) involves calculating torque when force is applied at the center of the door. - Part (b) involves calculating torque when force is applied at the edge of the door. Both scenarios emphasize understanding how the point of force application affects the torque on the door.
Expert Solution
Step 1

Given value---

  • length = 1.3 m.
  • Force = 34.5 N.
  • force is acting perpendicular to door length. 

We have to find---

  • (a) What magnitude of torque (in N. m) is applied about an axis through the hinges?
  • (b) What magnitude of torque (in N m) is applied about the axis through the hinges now?

 

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