The drawing shows a bicycle wheel resting against a small...

The drawing shows a bicycle wheel resting against a small step whose height is $h=0.120 \mathrm{m}$. The weight and radius of the wheel are $W=25.0 \mathrm{N}$ and $r=0.340 \mathrm{m},$ respectively. A horizontal force $\overrightarrow{\mathbf{F}}$ is applied to the axle of the wheel. As the magnitude of $\overrightarrow{\mathbf{F}}$ increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens?

Key Concepts

Static Equilibrium

Static equilibrium refers to the state of an object where it remains at rest, meaning that both the net force and the net torque acting on it are zero. In this context, ensuring that the opposing torques due to the applied force and the weight of the wheel balance is central to determining the threshold at which the wheel begins to tip.

Pivot Analysis

Pivot analysis involves choosing an appropriate point about which to sum the torques, typically where friction or support forces act. For a wheel in contact with a step, analyzing torques about the step edge simplifies the problem by eliminating the contribution of the contact force at that specific point, helping to isolate the effects of the applied force and the weight.

Torque Equilibrium

Torque equilibrium is the condition where the sum of all torques about a chosen pivot point is zero. In problems where an object is on the verge of rotating, such as a wheel beginning to rise over a step, setting the net torque to zero allows one to determine the critical conditions under which rotation (or tipping) occurs.

Lever Arm

The lever arm is the perpendicular distance from the line of action of a force to the pivot point. It is crucial in calculating torques because even a small force can produce a significant rotational effect if its lever arm is long. Correctly identifying these distances is key to solving problems involving rotational motion.

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