Academic Physics Spring Final - Energy Review Notes

Work

• Work is done when:
  • There is a force that causes an acceleration.
  • The force and displacement are in the same direction (parallel).
  • There is a change in kinetic energy.
• Net work done on the baby being carried:
  • The parent is carrying their 7 kg baby 50 meters down the sidewalk.
  • The net work done on the baby is 0 J because the force applied by the parent is vertical, while the displacement is horizontal.
• Work done by a force:
  • The graph shows the force exerted on a block as a function of the block’s displacement in the direction of the force.
  • The work is the area under the curve.
  • The work done in moving the block to 20 meters is 100 J.

Power

• Power is the rate at which work is done.
• How much power is exerted when a 100-pound student walks 15 feet up the stairs in 9 seconds?
  • The power exerted is 167 ftlb/s.

Kinetic Energy

• Kinetic Energy Formula: $KE = (1/2) * mv^2$, where $m$ is the mass and $v$ is the speed.
• The table below lists the mass and speed of four objects. Which object has the most kinetic energy?

Potential Energy

• Gravitational Potential Energy: $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (approximately 9.8 m/s²), and $h$ is the height.
• A 0.5 kg basketball is thrown upwards. What is the potential energy of the basketball at the top of its path if it reaches a height of 5 m?
  • The potential energy of the basketball at the top of its path is 24.5 J.
• Pendulum Motion:
  • As a pendulum moves from the bottom of its swing to the top of its swing, the kinetic energy of the pendulum decreases.

Spring Potential Energy

• Spring Potential Energy: $PE = (1/2) * k * x^2$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position.
• In the accompanying diagram, a student compresses the spring in a pop-up toy 0.020 meters. If the spring has a spring constant of 499 N/m, how much energy is being stored in the spring?
  • The energy is being stored in the spring is 0.0998 J.

Roller Coaster

• Total Mechanical Energy: $E = KE + PE$ . Where KE is kinetic energy and PE is potential energy.
• A 550 kg roller coaster travels along the track pictured below.
  • The total mechanical energy of the roller coaster is 150920 J.
  • The potential energy of the roller coaster at point B is 26950 J.
  • The kinetic energy of the roller coaster at point B is 123970 J.
  • The roller coaster is moving at point B is 21 m/s.