Summary Slides - Vertical + Horizontal UCM

Apparent Weight

  • Definition: Apparent weight is the sensation of weight experienced by a person or object due to the normal force exerted by a surface. This sensation can change based on various forces acting during motion.

Experience in Motion

  • When traveling in a vehicle (car/bus) over hills/dips, occupants may feel lighter or heavier.

  • This phenomenon is due to a change in the normal force acting on the occupants as a result of acceleration changes.

Free Body Diagrams and Forces

  • Normal Force (FN): The upward force opposing the object's weight (mg).

  • Weight (W): The force of gravity acting downward.

  • When normal force decreases or equals zero, the object experiences 'weightlessness'.

Changes in Apparent Weight

  • Example: In airplanes, passengers can feel 'weightless' during certain maneuvers.

Circular Motion

  • Objects moving over a hilltop can be analyzed as undergoing Uniform Circular Motion (UCM).

  • At the top of a circular vertical path, both the car's weight and acceleration direct downwards while the normal force acts upwards.

Newton’s Second Law Application

  • At the top of the curve, the net force equation can be formulated:

    [ a = v^2 / r ]

    [ W - FN = ma ] (where W = mg)

  • Rearranging gives insights on how apparent weight changes as speed alters.

Calculating Apparent Weight

  • The normal force can decrease until zero, resulting in zero apparent weight when the centripetal force is equal to the weight.

  • To find this minimum speed at which an object feels weightless:

    • Set FN = 0 and solve for speed (v).

Bottom of Circular Path

  • When driving into a dip, both normal force and centripetal acceleration act upwards.

  • Forces involved:

    • FN (up) > W (down) results in increased apparent weight.

  • At high speeds, this results in higher apparent weight values.

Bucket on a Rope - An Example of Circular Motion

  • Forces on a Bucket:

    • At the bottom: Tension (FT) + Weight (mg) determine the net upward force.

    • At the top: Both forces act down, but the bucket maintains enough speed to keep water inside.

Minimum Velocity Condition

  • If tension (FT) becomes zero at the top of the circular path, the bucket will no longer maintain a circular path, and the water will fall out.

Roller Coasters and Circular Motion

  • Similar principles apply to roller coasters:

    • The normal force from the track provides the centripetal force necessary to keep the ride on its path.

  • At the top of a loop, if FN = 0, the car becomes weightless.

Forces At Loop Points

  • At the bottom of the loop, the normal force must be greater than gravitational force for the occupants to feel a sensation of weight.

Applying Concepts of Circular Motion

  • Calculate minimum centripetal acceleration necessary for maintaining contact with the track.

  • Understand the critical balance of forces in both upward and downward positions for both the bucket and roller coaster.

Summary of Key Concepts

  • Apparent weight varies with normal force and the direction of motion.

  • Circular motion influences both normal and apparent weight in vehicles and amusement rides, emphasizing the role of speed and gravitational force.