The figure shows a bicycle wheel resting against a small step whose height is h = 0.110 m. The weight and radius of the wheel are W = 26.0 N and r = 0.370 m. A horizontal force is applied to the axle of the wheel. As the magnitude of 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?
To find the magnitude of the force when the wheel just begins to rise up and loses contact with the ground, we can analyze the forces acting on the wheel.
The weight of the wheel, W, acts downward and is given as 26.0 N. The normal force, N, acts upwards perpendicular to the ground.
When the wheel is on the verge of losing contact with the ground, the normal force is equal to zero. This means that the weight of the wheel is balanced by the force applied to the axle.
Using Newton's second law, we can express this as:
ΣF = ma
Where ΣF is the sum of the forces acting on the wheel, m is the mass of the wheel, and a is the acceleration of the wheel.
Since the wheel is not accelerating vertically, the sum of the vertical forces is equal to zero:
N - W = 0
N = W
Therefore, the force at which the wheel just begins to rise up and loses contact with the ground is equal to the weight of the wheel, which is 26.0 N.
To find the magnitude of the force required for the wheel to just begin to rise up and lose contact with the ground, we need to consider the equilibrium condition.
When the wheel is about to lose contact with the ground, the normal force exerted by the ground on the wheel becomes zero. The weight of the wheel provides a downward force, and the applied horizontal force provides an upward force.
Let's break down the forces acting on the wheel:
1. Weight (W): This is the force pulling the wheel downward. The weight of the wheel is given as W = 26.0 N.
2. Normal force (N): This is the perpendicular force exerted by the ground on the wheel. When the wheel is about to lose contact with the ground, N = 0.
3. Applied force (F): This is the horizontal force applied to the axle of the wheel. This is the force we are trying to find.
Since the wheel is in equilibrium, the sum of the forces in the vertical direction must equal zero:
ΣFy = N - W = 0
N = W
Substituting the given value for the weight of the wheel, N = 26.0 N.
Since the normal force is equal to the weight, the maximum applied force required to just begin to lift the wheel is the force needed to overcome the weight:
F = W = 26.0 N
Therefore, the magnitude of the force required for the wheel to just begin to rise up and lose contact with the ground is 26.0 N.