Work and Kinetic Energy

1. Work and Kinetic Energy • Work by a variable force • Kinetic Energy and the Work-Energy Theorem • Power Serway & Jewett 7.3, 7.4 Physics 1D03

2. Determine the work done by a force as the particle moves from x=0 to x=6m: F(N) 5 x(m) 0 1 2 3 4 5 6 Physics 1D03

3. Kinetic Energy Definition: for a particle moving with speed v, the kinetic energy is K = ½ mv2 (a SCALAR) Then the Work-Energy Theorem says: The total work done by all external forces acting on a particle is equal to the increase in its kinetic energy. Proof: from Newton’s Second Law, and the definition of Work. Physics 1D03

4. Kinetic Energy is measured in joules (1J=1Nm). • Kinetic energy is a scalar; the work-energy theorem is a scalar relation. • This theorem is equivalent to Newton’s Second Law. In principle, either method can be used for any problem in particle dynamics. • The energy approach works most easily with forces and velocities as functions of position, rather than time. Physics 1D03

5. Example A block of mass 1kg moving with vi=2m/s gets a push of 10N over a distance of 4m. What is the new velocity ? Physics 1D03

6. Example A bartender slides a 1-kg glass 3 m along the bar to a customer. The glass is moving at 4 m/s when the bartender lets go, and at 2 m/s when the customer catches it. Find the work done by friction, and calculate the force of friction. Physics 1D03

7. Quiz A spring is hanging vertically. A student attaches a 0.100-kg mass to the end, and releases it from rest. The mass falls 50 cm, stretching the spring, before stopping and bouncing back. During the 50-cm descent, the total work done on the mass was: • zero • 0.49 J • -0.49 J • none of the above Physics 1D03

8. Power Power is the rate at which work is done: units: 1 J/s =1 watt (W) Average power = Work/Time Instantaneous power: infinitesimal time dt, displacement dr; work dW = F.dr, and power is Physics 1D03

9. Example • A 100kg block is pulled at a constant speed of 5.0m/s across a horizontal floor by force of 122N directed 37º above the horizontal. • What is the power supplied by the force? • Where does the energy go? Physics 1D03

10. 122N a) Free body diagram. b) The table (friction) does negative work on the block. The frictional work transfers energy to the random thermal motion of atoms of the block, table & air. n 37º v=5.0 m/s mg Physics 1D03

11. Concept Quiz A 2000-kg elevator starts from rest and moves upwards with a constant acceleration of 1.0 m/s2. The power required from the motor • Increases with time, starting from zero • Is large as soon as the elevator starts, then decreases with time • Is constant after the elevator starts to move. Physics 1D03

12. Quiz • A 100-kg sprinter accelerates from rest to 10 m/s in 4 seconds. His average power output is about: • 2.5 W • 1.25 kW • 50 kW • It depends on whether accleration is constant Physics 1D03

13. Quiz The resistance to the motion of a racing bicycle on a smooth level road is mostly due to air resistance. The force of air resistance is proportional to the square of the speed (Fair ~ v2). A cyclist uses 500 W of power to ride at 50 km/h. What power does he need to ride at 30 km/h ? • 300 W • 180 W • 108 W Physics 1D03

14. Summary • Work: • To stretch an ideal spring: W = ½ kx2 • Kinetic Energy:K = ½ mv2 • Work-energy theorem:The total work is equal to the change in kinetic energy. Physics 1D03