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.