A 0.087 kg remote control 16.7 cm long rests on a table, as shown in the figure below, with a length L overhanging its edge. To operate the power button on this remote requires a force of 0.470 N Assume the mass of the remote is distributed uniformly, and that the power button is on the end of the remote overhanging the table. a.) How far can the remote control extend beyond the edge of the table and still not tip over when you press the power button? cm b.) How large is the normal force when the button is pressed? N (How would this answer change if the remote were not at maximum extension?)

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**Physics Problem: Stability and Forces on a Remote Control**

A 0.087 kg remote control, 16.7 cm long, rests on a table as shown in the figure below, with length \( L \) overhanging its edge. To operate the power button on this remote requires a force of 0.470 N. Assume the mass of the remote is distributed uniformly, and that the power button is on the end of the remote overhanging the table.

**Diagram Explanation:**

The diagram illustrates a remote control partially overhanging a table. The part of the remote that extends beyond the table is labeled as length \( L \). A hand is depicted pressing the power button located at the overhanging end of the remote.

**Questions:**

a.) How far can the remote control extend beyond the edge of the table and still not tip over when you press the power button?

[Input Box] cm

b.) How large is the normal force when the button is pressed?

[Input Box] N

*(How would this answer change if the remote were not at maximum extension?)*

---

**Considerations:**

- The uniform distribution of mass implies that the center of mass of the remote is at its midpoint when fully on the table.
- The pressing force applied at the end may cause the remote to tip if the torque about the edge of the table surpasses the counteracting torque due to the remote’s weight.
- Calculate the equilibrium point where the torque induced by pressing the button equals the torque due to the weight distribution.
Transcribed Image Text:**Physics Problem: Stability and Forces on a Remote Control** A 0.087 kg remote control, 16.7 cm long, rests on a table as shown in the figure below, with length \( L \) overhanging its edge. To operate the power button on this remote requires a force of 0.470 N. Assume the mass of the remote is distributed uniformly, and that the power button is on the end of the remote overhanging the table. **Diagram Explanation:** The diagram illustrates a remote control partially overhanging a table. The part of the remote that extends beyond the table is labeled as length \( L \). A hand is depicted pressing the power button located at the overhanging end of the remote. **Questions:** a.) How far can the remote control extend beyond the edge of the table and still not tip over when you press the power button? [Input Box] cm b.) How large is the normal force when the button is pressed? [Input Box] N *(How would this answer change if the remote were not at maximum extension?)* --- **Considerations:** - The uniform distribution of mass implies that the center of mass of the remote is at its midpoint when fully on the table. - The pressing force applied at the end may cause the remote to tip if the torque about the edge of the table surpasses the counteracting torque due to the remote’s weight. - Calculate the equilibrium point where the torque induced by pressing the button equals the torque due to the weight distribution.
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