A cyclist is attached to a rope which is looped over a pulley (disc of mass 10kg and radius 0.5m). The rope is then

attached to a hanging block of mass 5kg. What force must the cyclist generate such that the block will move with an
acceleration of 2.25 m/s2. Let’s make the assumption that only one wheel of the bicycle is necessary to generate the
force (we can ignore the front wheel) and that all the force will manifest itself in rolling friction. The mass of the
bicycle and the cyclist is 90kg. The surface has a coefficient of static friction of 0.65 and kinetic friction of 0.25.

Any thoughts?

To find the force that the cyclist must generate, we need to consider the forces acting on the system.

1. Force of gravity on the hanging block: The force of gravity can be calculated using the equation F_gravity = mass * acceleration due to gravity. In this case, the mass of the hanging block is 5 kg, and the acceleration due to gravity is approximately 9.8 m/s². So, the force of gravity on the hanging block is F_gravity = 5 kg * 9.8 m/s² = 49 N.

2. Force required to overcome the static friction: The static friction force is responsible for preventing the block from moving initially. The maximum static friction force can be calculated using the equation F_static_friction = coefficient of static friction * normal force. The normal force is the force exerted by the pulley on the rope and is equal in magnitude but opposite in direction to the force of gravity on the hanging block. Therefore, the normal force is 49 N. Given that the coefficient of static friction is 0.65, the maximum static friction force is F_static_friction = 0.65 * 49 N = 31.85 N.

3. Force required to maintain the acceleration: Once the block starts moving, it experiences kinetic friction instead of static friction. The equation for the kinetic friction force is F_kinetic_friction = coefficient of kinetic friction * normal force. With a coefficient of kinetic friction of 0.25 and a normal force of 49 N, the kinetic friction force is F_kinetic_friction = 0.25 * 49 N = 12.25 N.

Since the force generated by the cyclist will be responsible for overcoming both the static and kinetic friction forces, the total force required can be calculated as follows:

Total force = Force of gravity on the hanging block + Force required to overcome static friction + Force required to maintain the acceleration
Total force = 49 N + 31.85 N + 12.25 N
Total force = 93.10 N

Therefore, the cyclist must generate a force of 93.10 N to move the block with an acceleration of 2.25 m/s².