Question

A 0.035 kg, 10 cm long TV remote control has a power button at the top. It takes 0.35 N of force to operate the power button. How far over the edge of a table could the power button extend for the remote to not fall when you push it with 0.33 N? Assume the mass of the remote is distributed uniformly.

A) 1.1 cm
B) 2.5 cm
C) 5.0 cm
D) 3.3 cm
E) 0.95 cm

Answer 1

The power button can extend up to approximately 0.96 cm over the edge of the table without the remote falling when pushed with a force of 0.33 N.

Among the given options, the closest answer is option E) 0.95 cm.

To determine how far over the edge of a table the power button can extend without the remote falling, we need to consider the balance of forces acting on the remote.

First, let's calculate the weight of the remote. Weight is equal to mass multiplied by the acceleration due to gravity
`(9.8 m/s^2)`. The mass of the remote is given as 0.035 kg, so its weight is 0.035 kg ×
`9.8 m/s^2` = 0.343 N.

Next, let's analyze the forces acting on the remote when the power button is pushed with a force of 0.33 N. The downward force of gravity is 0.343 N, and the upward force from pushing the power button is 0.33 N. Since the remote is not falling, these forces must be equal.

So, we have the equation:

0.343 N - 0.33 N = 0

To prevent the remote from falling, the net force must be zero. This means the pushing force must be equal to or greater than the weight of the remote. In this case, the pushing force is 0.33 N, which is less than the weight of the remote (0.343 N).

Since the pushing force is less than the weight of the remote, the remote will fall if the power button extends too far over the edge of the table. To find out how far the power button can extend, we need to calculate the lever arm (the perpendicular distance between the point of rotation and the line of action of the force).

The lever arm can be calculated using the formula:

Lever arm = Torque / Force

In this case, the torque is equal to the weight of the remote multiplied by the distance the power button extends over the edge of the table. Let's assume the power button extends x cm over the edge of the table.

So, the torque is 0.343 N × x cm. And the force is 0.33 N.

Using the formula, we have:

0.343 N × x cm / 0.33 N = x cm

Simplifying, we have:

0.343 N × x cm = 0.33 N

Dividing both sides by 0.343 N, we get:

x cm = 0.33 N / 0.343 N

x cm = 0.96 cm

Therefore, the power button can extend up to approximately 0.96 cm over the edge of the table without the remote falling when pushed with a force of 0.33 N.

Among the given options, the closest answer is E) 0.95 cm