Recording-2025-03-11T15:01:34.411Z

Zero Point in Physics

• When analyzing motion, choose a zero point (reference point) for potential energy.

  • Commonly, this is the lowest point of the movement.

  • The energy can be calculated as the change in potential and kinetic energy.

Understanding Initial Velocity and Angles

• If an object is thrown at an angle, break down its velocity:

  • Horizontal component: ( v_{hx} = v \cdot ext{cos}( heta) )

  • Vertical component: ( v_{hy} = v \cdot ext{sin}( heta) )

  • For horizontal motion, velocity remains constant (no air resistance).

  • Vertical motion is affected by gravity, causing the object to fall an additional distance equal to its height.

Energy Conservation in Motion

• The total energy (potential + kinetic) at the start equals the total energy just before impact:

  • Initial kinetic energy: ( KE_{initial} = \frac{1}{2} mv^2 )

  • Initial gravitational potential energy: ( PE_{initial} = mgh )

  • Final total energy before impact is kinetic as potential energy drops to zero.

Calculations for Kinetic and Potential Energy

• Given:

  • Mass of object: 250 grams (0.25 kg)

  • Initial height: 20 meters

  • Initial velocity: 10 meters/second

• Kinetic energy calculation:

  • ( KE_{initial} = \frac{1}{2} (0.25) (10^2) = 12.5 , J )

• Potential energy calculation:

  • ( PE_{initial} = (0.25)(9.8)(20) = 49 , J )

Energy Equivalence Just Before Impact

• At the moment just before impact:

  • Total initial energy = Kinetic energy just before impact

  • Kinetic energy just before impact: ( KE_{final} = KE_{initial} + PE_{initial} )

  • Thus, total initial energy: ( 12.5 , J + 49 , J = 61.5 , J )

Using Energy to Calculate Final Speed

• Use conservation of energy principles:

  • Total energy before = Total energy after, leading to:

  • ( KE_{final} = \frac{1}{2} mv_f^2 )

• Solve for final velocity:

  • ( v_f = \sqrt{2g(h_{initial})} )

• Example with height:

  • For height 11 cm (0.11 m), final velocity = ( v_f = \sqrt{2 imes 9.8 imes 0.11} = 1.5 , m/s )

Pendulum Analysis

• For a pendulum:

  • Energy conservation principles apply.

  • Height and energy trade-off from potential to kinetic energy.

• Height and speed relationship through conservation of mechanical energy:

  • Initial potential energy = Final kinetic energy and vice versa.

Spring Energy Storage

• When compressing a spring, energy stored as potential energy:

  • ( PE_{spring} = \frac{1}{2} k x^2 )

• Example with spring constant:

  • If ( k = 11 , N/m ), and spring is compressed 22 cm (0.22 m):

  • Potential energy = ( 0.27 , J ).

Transfer of Energy from Spring to Mass

• Energy in the compressed spring converts to kinetic energy of a mass when released:

  • ( PE_{spring} = KE_{final} )

  • Leads to velocity calculation for the mass based on energy equations.

Conclusion on Energy and Motion

• The conservation of energy applies across various motion scenarios:

  • As motion occurs, potential energy transforms into kinetic energy and vice versa.

  • Variances in height or energy mass lead to different speeds based on conservation of energy principles.