physics

• Work is done when a force applied to an object causes a displacement of the object
• Energy is defined as the capacity to do work
• Power is the work done per unit of time
• The amount of work done is not related to how tired you feel; work is only done when a force causes an object to move
• Work (W) is the product of the magnitude of the displacement (s) and the component of the force (F) in the direction of the displacement, W = Fs cos θ
• The unit of work is N - m in SI and ft - lb in the English system, with 1 Joule (J) equal to 1 N - m
• Power is a measure of how fast work is being done by a force
• Power (P) is defined as Work done (W) divided by elapsed time (t), P = W/t
• The unit of power in the SI system is watt (W), where 1 W = 1 J/s
• In the English system, the unit of power is ft - lb/s, and another unit is horsepower (hp), where 1 hp = 550 ft - lb/s
• The conversion factors between units are: 1 hp = 746 W = 0.746 kW, and 1 kW = 1.34 hp
• Energy is the ability to do work, and the units of energy are the same as work (joule and foot-pound)
• Kinetic energy (KE) is the energy of a moving object
• The work done on an object is equal to the change in its kinetic energy, W = ΔKE
• Kinetic energy (KE) formula: KE = 1/2 m (vf^2 - vi^2)
• Work done on an object is equal to the change in its kinetic energy
• The formula for work done on an object is: W = ΔKE = ½m(vf^2 - vi^2)
• Kinetic energy (KE) is calculated as KE = ½mv^2
• For a person weighing 80.0 kg running at 5.00 m/s, the kinetic energy is 1.00 x 10^3 J
• In the case of a baseball pitcher throwing a fastball at 90.0 mi/h and a ball weighing 0.250 lb:

  • Initial kinetic energy of the baseball is 67.6 ft-lb
  • Work done on the baseball by the catcher's mitt is -67.6 ft-lb
• To have the same kinetic energy as a 2.00 x 10^3 kg pickup truck moving at 90.0 km/h, a 1.00 x 10^3 kg sports car needs to be going at 35.4 m/s
• Potential energy (PE) of an object is the energy it has due to its position
• For a 5.00 lb object held at different heights:

  • Potential energy relative to the tabletop is 10.0 ft-lb
  • Potential energy relative to the floor is 25.0 ft-lb
  • Potential energy relative to the ground is 150 ft-lb
• Niagara Falls, with a drop of 160 ft, does 1.34 x 10^5 ft-lb of work as 100 gallons of water hit the base
• If a pile driver is raised to a height of 1.50 m with 115 kJ of work done, the mass of the pile driver is 7.82 x 10^3 kg
• The Law of Conservation of Energy states that the total amount of energy in a closed system is constant
• In a system, the total mechanical energy (E) is the sum of its kinetic energy and potential energy: E = PE + KE
• For a bead sliding on a wire with a speed of 200 cm/s at point A:

  • Speed at point B is 4.44 m/s
  • Speed at point C is 3.14 m/s
• For a 2 kg object dropped from a 100 m building:

  • Total mechanical energy at the top of the building is 1962 J
  • Gravitational potential energy at 2 m high before hitting the ground is 39.24 J
  • Kinetic energy at 2 m high before hitting the ground is 1922.76 J