Recording-2025-03-06T15:39:08.191Z

Force and Motion

• Once an object is in motion, no force is needed to maintain that sideways motion, as per Newton's First Law of Motion.

  • Example: If there is no friction, an object will continue moving sideways indefinitely.

Understanding Forces in a System

• When analyzing forces:

  • 2 N gravitational force downward and 2 N normal force upward counteract each other, leading to no movement in the vertical direction.

  • 400 N net force moving the box over a displacement of 5 m results in a work done of 2000 J.

  • The mass of the object (e.g., 75 kg vs. 1200 kg) does not directly impact the force required for sideways motion unless friction is involved.

Work Done by Force

• When a force is applied at an angle, only the component of the force in the direction of the displacement does work.

  • Work = Force x Displacement x cos(θ).

  • For instance: If a force of 150 N is applied at a 20-degree angle, you calculate the horizontal component using F_x = F * cos(θ):

    • F_x = 150 N * cos(20°).

Power and Time Relation

• Power is defined as work done over time and is given in watts (W), where 1 W = 1 J/s.

• The relationship between power and energy:

  • Energy = Power x Time.

    • For example, if 100 W is applied for 2 hours, the total energy used would be:

      • Energy = 100 W * 2 hours * 3600 seconds/hour = 720,000 J.

Units Conversion and Energy Charges

• Electric bills are generally charged in kilowatt-hours (kWh):

  • 1 kWh = 1,000 W for 1 hour = 3,600,000 J.

• This pricing structure uses kilowatt-hours for practicality, as joules represent a very large number for everyday use.

Kinetic and Potential Energy

• The kinetic energy (KE) of an object in motion is given as:

  • KE = (1/2)mv^2

• Example:

  • A 94.6 kg watermelon has 4500 J of kinetic energy, which allows calculation of its velocity (v).

    • By rearranging the kinetic energy formula: v = sqrt((2 * KE) / m).

Conservation of Energy Law

• The principle states that total energy remains constant; energy can neither be created nor destroyed, only converted from one form to another.

• For example, when an object slides frictionlessly down a slide, its potential energy is converted into kinetic energy.

Work-Energy Principle

• The work done on an object equals the change in its kinetic energy:

  • W = ΔKE = KE_final - KE_initial.

  • If starting at rest, KE_initial = 0, thus, KE_final = W.

Practical Examples of Energy Calculation

• Example scenario: Dropping a mass gives it kinetic energy equal to the gravitational potential energy at its height:

  • PE = mgh = KE at the bottom.

• If dropped from 1.5 m, a mass will have a calculated final velocity using energy conservation.

Identifying Mistakes in Calculations

• Accurate unit management is crucial; ensure that the units align correctly when performing energy and force calculations to avoid errors.