Question

A0.122 kg remote control 220cth long rests on a table. as thown in the figure[figure 1). with a length L Part A overhanging on the edge. To operate the power button on this remote requires a force of 0.355 N How far can the remote control extend beyond the edge of the table and still not tip over when you press the power button? Assume the mass of the remote is distributed uniformly, and that the power button is 1.51 cm from the overtanging end of the remote.

Answer 1

To find how far the remote can overhang without tipping when the power button is pressed, one must equate the torque from the remote's weight with the torque from the applied force and solve for the overhanging distance.

Step-by-step explanation:

The problem requires finding how far the remote control can extend over the edge of the table without tipping when force is applied to press the power button. Lever principle and rotational equilibrium concepts apply here. The torque caused by the mass of the remote must balance with the torque caused by the force on the power button to prevent tipping.

Since the mass (0.122 kg) is uniformly distributed, the center of mass is at the middle of the remote, i.e., 110 mm from either end. When the button is pressed with a force of 0.355 N at a point 15.1 mm from the overhanging end, the torque about the edge of the table due to this force can be calculated. The maximum overhang occurs when the torque from the weight of the remote is exactly equal to the torque from pressing the button.

The torque due to the remote's weight (torque weight) = mass × gravity × distance from the pivot to the center of mass. Torque due to the applied force (Torqueforce) = force × distance from the pivot to the point of application of force.

Setting Torqueweight equal to Torqueforce and solving for the overhanging distance (L) gives us the maximum distance before tipping. Here gravity is 9.8 m/s2.