2Energy Topics 5-01 Work 5-02 Kinetic Energy & the Work Energy Theorem 5-03 Gravitational Potential Energy5-04 Spring Potential Energy5-05 Systems and Energy Conservation5-06 PowerEnergy
3WorkThe work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:Energy
4WorkWhat is the correct unit of work expressed in SI units?(A) kg m2/s2(B) kg m2/s(C) kg m/s2(D) kg2 m/s2
5WorkHow much work did the movers do (horizontally) pushing a 160 kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?
6WorkCan work be done on a system if there is no motion?(A) Yes, if an outside force is provided.(B) Yes, since motion is only relative.(C) No, since a system which is not moving has no energy.(D) No, because of the way work is defined.
7Object falls in a gravitational field WorkObject falls in a gravitational fieldmmghmWg = mghEnergy
8WorkA 50 N object was lifted 2.0 m vertically and is being held there. How much work is being done in holding the box in this position?(A) more than 100 J(B) 100 J(C) less than 100 J, but more than 0 J(D) 0 J
9WorkWork done by forces that oppose the direction of motion, such as friction, will be negative.fvdvFcCentripetal forces do no work, they are always perpendicular to the direction of motion.Energy
10WorkDoes a centripetal force acting on an object do work on the object?(A) Yes, since a force acts and the object moves,and work is force times distance.(B) No, because the force and the displacementof the object are perpendicular.(C) Yes, since it takes energy to turn an object.(D) No, because the object has constant speed.
11Friction acts on moving object WorkFriction acts on moving objectmmfdEnergy
12WorkThe area under the curve, on a Force versus position (F vs. x) graph, represents(A) work.(B) kinetic energy.(C) power.(D) potential energy.
13WorkOn a plot of Force versus position (F vs. x), what represents the work done by the force F?(A) the slope of the curve(B) the length of the curve(C) the area under the curve(D) the product of the maximum force times the maximum x
14Kinetic Energy and the Work Energy Theorem Force acts on a moving objectvfviKineticEnergyFmxEnergy
15Kinetic Energy and the Work Energy Theorem (Problem) A baseball (m = 140 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?
16Kinetic Energy and the Work Energy Theorem The quantity is(A) the kinetic energy of the object.(B) the potential energy of the object.(C) the work done on the object by the force.(D) the power supplied to the object by the force.
17Kinetic Energy and the Work Energy Theorem (Problem) (a) If the KE of an arrow is doubled, by what factor has its speed increased?
18Kinetic Energy and the Work Energy Theorem (Problem) (b) If the speed of an arrow is doubled, by what factor does its KE increase?
19Kinetic Energy and the Work Energy Theorem Work done is equal to the change in the kinetic energy:If the net work is positive, the kinetic energy increases.If the net work is negative, the kinetic energy decreases.Energy
20Gravitational Potential Energy When an object is thrown upward.Positive workdone by thegravitationalforceNegative workdone by thegravitationalforceEarthEnergy
21Gravitational Potential Energy An object can have potential energy by virtue of its position.Familiar examples of potential energy:A wound-up springA stretched elastic bandAn object at some height above the groundEnergy
22Gravitational Potential Energy In raising a mass m to a height h, the work done by the external force isy2FextmhmgWe therefore define the gravitational potential energy:y1Energy
23Gravitational Potential Energy The quantity is(A) the kinetic energy of the object.(B) the gravitational potential energy of the object.(C) the work done on the object by the height.(D) the power supplied to the object by the force.
24Gravitational Potential Energy (Problem) How high will a 1.85 kg rock go if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.
26Spring Potential Energy The restoring force of a spring iswhere k is called the spring constant, and needs to be measured for each spring.The force required to compress or stretch a spring is:Energy
27Spring Potential Energy The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written:FxWorkkxEnergy
28Spring Potential Energy The quantity is(A) the kinetic energy of the object.(B) the elastic potential energy of the object.(C) the work done on the object by the displacement.(D) the power supplied to the object by the force.
29Spring Potential Energy (Problem) A spring (with k = 53 N/m) hangs vertically next to a ruler. The end of the spring is next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?Energy
30Systems and Energy Conservation The sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign.This allows us to define the total mechanical energy:And its conservation:Energy
31Systems and Energy Conservation If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.yEnergy
32Systems and Energy Conservation Ball dropped from rest falls freely from a height h.Find its final speed.hvEnergy
33Systems and Energy Conservation A block of mass m compresses a spring (force constant k) a distance x. When the block is released, find its final speed.vmmxEnergy
34Systems and Energy Conservation When released from rest, the block slides to a stop.Find the distance the block slides.vf = 0Friction (m)mmkxdEnergy
35Systems and Energy Conservation A block released from rest slidesfreely for a distance d.vi = 0mdhmqV = ?Find the final speed of the blockh = d sin(q)Energy
36Power is the rate at which work is done – In the SI system, the units of power are Watts:The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.Energy
37PowerPower is also needed for acceleration and for moving against the force of gravity.The average power can be written in terms of the force and the average velocity:vFFrdEnergy
38Power (Problem)A 1000 kg sports car accelerates from rest to 20 m/s in 5.0 s. What is the average power delivered by the engine?Fnet = maa = (20m/s – 0)/5.0s = 4.0 m/s2Fnet = (1000 kg)(4.0 m/s2) = 4000 NP = FvaveP = (4000N)[( m/s)/2]P = (4000N)(10 m/s)Power =40,000 WEnergy