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Understanding the concept of normal force is important in scenarios involving circular motion. Normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the surface is the track of the circular path. When a block moves in a vertical circle, the normal force varies based on its position in the path.
At the bottom of the path (point A), the normal force is higher because it has to support not only the weight of the block but also provide the centripetal force required to keep it moving in a circle. The equation at point A is:

• \( F_{N_A} = m imes g + \frac{m imes v_A^2}{R} \)

At the top of the path (point B), the normal force decreases. Here, gravity and the velocity provide the necessary centripetal force, reducing the normal force:

• \( F_{N_B} + m \cdot g = \frac{m \cdot v_B^2}{R} \)

Normal force decreases at the top because gravity also acts in the direction needed for circular motion.

Kinetic energy is a type of energy an object possesses due to its motion. In a circular motion scenario, the kinetic energy of an object is influenced by its speed. The formulas for kinetic energy at different points in the motion (A and B in this exercise) are given as:

• At point A: \( KE_A = \frac{1}{2} m v_A^2 \)
• At point B: \( KE_B = \frac{1}{2} m v_B^2 \)

The key idea here is that as the block moves from the bottom to the top of the circle, its velocity changes, and so does its kinetic energy. The change in velocity is due to the work done by forces during its motion. It's essential to calculate the velocities at both these points to determine their respective kinetic energies, reflecting the object's ability to perform work.

The work-energy principle is a fundamental concept in physics. It relates the work done by forces acting on an object to the change in its kinetic energy. For a block moving in a vertical circle, as in this exercise, the principle can be used to calculate the work done by friction.After determining the kinetic energy at points A and B, the change in kinetic energy \( \Delta KE \) can be found. The formula for the work done by friction is:

• \( W_{friction} = \Delta KE + m \cdot g \cdot (2R) \)

Here, \( m \cdot g \cdot (2R) \) represents the gravitational potential energy change, accounting for the height difference of \( 2R \) as the block moves from point A (bottom) to point B (top). The work-energy principle thus provides a comprehensive approach to finding the work done, by including changes in both kinetic and potential energy within the system.