Work What will happen when a force is applied to a mass moving at constant velocity? a v d –acceleration exists and displacement is covered

Work v f 2 – v i 2 = 2 ad Substitute Newton’s 2 nd law into the equation: a = F/m v f 2 – v i 2 = 2 (F/m)d Multiply both sides by m and divide by 2 ½ m (v f 2 – v i 2 ) = F d ½ m v f 2 – ½ mv i 2 = F d KE f – KE i = F d } Work - Energy Theorem

Work Work – the product of a force and a displacement of an object, in the same direction of motion. Work done – the process of changing the energy of a system Work is a scalar quantity because there is no direction Units : Joules = N m Work is only done if the force is the same direction as the motion If force is  to the motion, no work is done

Work Work done when force is at an angle… Fd Only the force acting in the direction of motion matters. W = F dW = F cos  d W = Fd cos 

Work Work done when force changes… You can determine the amount of work done on an object by graphing force versus distance.F Work d

Work Compressed Springs: (Recall Hooke’s Law) The force varies linearly with the elongation of the spring FW = ½ F x F= kx W = ½ (kx) x xW = ½ k x 2

Work Work done on a spring = the energy stored in a spring W = PE s = ½ k x 2 PE s = elastic potential energy (see handout on springs) Energy is stored in a spring in the compressed or elongated position. At equilibrium, there is no stored energy. If the spring is vibrating, it is here that the kinetic energy is maximum.

Power The time in which a force acts on a body (does work) determines the amount of power consumed. Power – the rate at which work is done (or energy is transferred.) P = W/tunits: Watts or J/s One Watt is relatively small so the kW is used 1 kW = 1000 W

Power What does the kWhr measure? Energy Derive the equation now…

Energy Gravitational Potential Energy If the reference frame chosen is an object and the Earth, the gravitational pull supplies the Force. (F=mg) The distance away from the surface of the Earth is the distance covered. (h) Work done = P.E. gained F d = m g h

Energy Conservation of Energy In a closed system, energy can change form, but the total amount of energy is constant Form change:W =  KE =  mgh = PE s In a closed system, Mechanical Energy (E) is constant: KE + PE = E = constant A change in PE is always accompanied by an increase in KE and vice versa

Energy In the absence of friction: the path the object takes does not affect the final KE or PE Ke i d h (mgh) KE f

Energy Work and energy in the presence of friction: Work done on the incline = PE gained Therefore, W – PE = work done by friction d h

Energy So what is the benefit of the incline if work done up the ramp is more than to just lift it? By lengthening the incline, d increases and the applied force is LESS Also, it would take longer to climb the incline via the ramp so the power is LESS (P = W/t = mgh/t)

Roller Coasters 1. Determine the total energy of the system KE + PE = E 2. At the ground level, all of the PE becomes KE because h=0 KE + 0 = E 3. On a smaller hill, some PE is gained so, KE + PE = E (see handout)