Work and Energy

Section Objectives: Define work by relating it to force and displacement. Identify where work is being performed in a variety of situations. Calculate the net work done when many forces are applied to an object.

When is work done on an object?  Work is done when a force causes a displacement of the object, and when components of a force are parallel to displacement.  Work = Force x Distance (W=Fxd)  The product of the component of a force along the direction of displacement and the magnitude of the displacement.  W=FdcosΘ, W net =F net dcosΘ  W=Nxm or Joules

How much work is done on a vacuum cleaner pulled 3.0-m by a force of 50.0-N at an angle of 30° above the horizontal? Knowns: d=3.0-m, F=50.0-N, Θ=30° Unknown: W=? Formula:_____________?

Work is a scalar quantity so it can be positive or negative. Work is positive when the component of force is in the same direction as the displacement. It is negative when the force is in the opposite direction of the displacement. CosΘ is negative for angles greater than 90°, but less than 270°.

Objectives: Identify several forms of energy. Calculate kinetic energy for an object. Apply the work-kinetic energy theorem to solve problems. Distinguish between kinetic and potential energy. Classify different types of potential energy. Calculate the potential energy associated with an object’s position.

KE=1/2mv 2 W net =FΔX=maΔX *For an object under constant acceleration, v f 2 =v i 2 +2aΔX W net =m(v f 2 -v i 2 )/2 W net =1/2mv f 2 -1/2mv i 2

A 7.0-kg bowling ball moves at 3.0-m/s. How fast must a 2.45-g table tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table tennis ball in play? Knowns: m b =7.0-kg, m t =2.45-g, v b =3.0-m/s Unknown: v t

W net =ΔKE

On a frozen pond, a person kicks a 10.0-kg sled, giving it an initial speed of 2.2-m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10? Known: m=10.0-kg, v i =2.2-m/s, v f =0-m/s, µ k =0.10 Unknown: d=?

Potential Energy-the energy of an object due to its position, shape, or condition.  Gravitational potential energy-the energy of an object due to its position relative to a gravitational source.  Pe g =mgh (h=height)  Elastic potential energy-the energy available for use when a deformed elastic object returns to its original configuration, compressed or stretched.  Pe elastic =1/2kx 2

A 70.0-kg stuntman is attached to a bungee cord with an unstretched length of 15.0-m. He jumps off a bridge spanning a river from a height of m. When he finally stops, the cord has a stretched length of 44.0-m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant (k) of the bungee cord is 71.8-N/m, what is the total potential energy relative to the water when the man stops falling?

Section Objectives: Identify situations in which conservation of mechanical energy is valid. Recognize the forms that conserved energy can take. Solve problems using conservation of mechanical energy.

If something is conserved, it remains constant. Mechanical energy is the sum of kinetic energy and all the forms of potential energy. Energy conservation occurs when acceleration varies.

Mechanical Energy is often conserved.  Me i =Me f Energy Mechanical Kinetic Mechanical PE gravitational PE elastic Non- mechanical All other forms

1/2mv i 2 + mgh i = 1/2mv f 2 + mgh f Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00-m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0-kg. Known: h i =3.0-m, m=25.0-kg, v i =0-m/s, h f =0-m Unknown: v f =?

Section Objectives: Relate the concepts energy, time, and power. Calculate power in two different ways. Explain the effect of machines on work and power.

P=W/Δt, W=Fd, P=Fv The SI unit of power is the watt, W. One watt is equal to one Joule per second.

A kg curtain needs to be raised 7.5-m, at constant speed, in as close to 5.0-s as possible. The power ratings for three motors are listed as 1.0-kW, 3.5-kW, and 5.5-kW. Which motor is best for the job? Known: m=193-kg, Δt=5.0-s, d=7.5-m Unknown: P=?