Chapter 5 – Work and Energy

Section 5-1 Work

work – a force applied through a distance

· if the object doesn’t move then no work is done

· only the component of the force that is in the direction of motion does work

· if more than 1 force is present on an object, first find the NET FORCE in the direction of the displacement

W = F ∙ d

This is called the dot product of two vectors.

Recall from pre-calc, to find the dot product, multiply the magnitude of the vectors by the cosine of the angle between them.

W = || F|| ||d|| cos θ

W_net = F_net d cos θ

· work is a scalar quantity

· work can be positive or negative (see p. 170)

Units for work:

SI Nm = 1 J J stands for Joule

english ft lbs

example: A 20.0 kg suitcase is lifted vertically 1m, then carried 5m across a room, then lifted 0.75m to a shelf. What is the total work done on the suitcase?

Section 5-2 Energy

kinetic energy – the energy of an object due to its motion

KE = ½ mv²

a scalar quantity

unit is Joule ( or Nm)

example: A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?

Work-kinetic energy theorem – the net work done on an object is equal to the change in the kinetic energy of the object

W_net = ΔKE

example: 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?

potential energy (PE) – the energy associated with an object due to the position of the object in relation to a reference point

· also referred to as “stored energy”

gravitational potential energy (GPE) – the potential energy associated with an object due to the position of the object relative to the Earth or some other gravitational source

PE_g = mgh

elastic potential energy – the potential energy in a stretched or compressed elastic object

PE_elastic = ½ kx²

k - the spring constant (or force constant)

· depends on the characteristics of the spring

· flexible – small k

· stiff – large k

· units for k are N/m

x - the distance the spring is compressed (or stretched) from its relaxed position (equilibrium)

example: When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.

a. What is the PE_g associated with this mass relative to the table?

b. What is the springs PE_elastic if k = 400N/m?

c. What is the total potential energy of the this system?

Section 5 -3 Conservation of Energy

conserve – to remain constant even though form may change

mechanical energy – the sum of kinetic energy and all forms of PE

ME = KE + ΣPE

ME is a way of classifying energy; NOT a new form of energy.

nonmechanical energy – nuclear, chemical, electrical, internal – these are ignored for our purposes

Conservation of Mechanical Energy: In the absence of friction, the total ME for a closed system remains the same. ME may change form, but the sum is constant.

ME_i = ME_f

example: A small 10.0 g ball is held to a slingshot that is stretched 6.0cm. The spring constant for the slingshot is 200N/m.

a. What is the elastic PE of the slingshot before release?

b. What is the KE of the ball just after the slingshot is released?

c. What is the balls speed at that instant?

d. How high does the ball rise if it is shot directly upward?

Sec. 5-4 Power

power – the rate at which energy is transferred

- the rate at which work is done

P = W/ Δt

when the force and displacement are perpendicular

P = Fd/Δt

which leads to

P = Fv

SI unit: J/s or a Watt (W)

english unit: horsepower 1hp = 746 W

ex: Two kids pull with forces of 250N in the same direction on a cart at a speed of 2m/s for 10 min.

a. Calculate the power delivered by the kids.

b. How much work is done by the kids?