2 EnergyEnergy can be thought of as a quantity that reflects the state of an objectThere are many different forms of energy, we will study mechanical energy:Kinetic Energy energy due to motionPotential Energy energy due to position in a “force field”
3 WorkWork is the amount of energy that is given to or taken from an object/systemIt is a scalar quantity has no directionIf energy is added to work is positiveIf energy is taken from work is negativeIt is measured in Joules (1 J = 1 kg.m2/s2)
4 Work done by a constant force Only valid when the force is constant, so you can’t use it when the force depends on the position (e.g. when attached to a spring)ϕ represents the smaller of the two angles between the Force and displacement vectorsIt has a range: 0° ≤ ϕ ≤ 180°
5 Work done by a constant force , special cases When the force is parallel to the displacement (ϕ=0°):When the force is antiparallel to the displacement (ϕ=180°):
10 Example 8-1An intern pushes a 72-kg patient on a 15-kg gurney, producing an acceleration of 0.60 m/s2. How much work does the intern do by pushing the patient and gurney through a distance of 2.5 m?
11 Example 8-2In a gravity escape system (GES), an enclosed lifeboat on a large ship is deployed by letting it slide down a ramp and then continuing in free fall to the water below. Suppose a 4970-kg lifeboat slides a distance of 5.00 m on a ramp, dropping through a vertical height of 2.50 m. How much work does gravity do on the boat?
12 Example 8-3 Work done by gravity is independent of the path! You want to load a box into the back of a truck. One way is to lift it straight up through a height h, as shown, doing a work W1. Alternatively, you can slide the box up a loading ramp a distance L, doing work W2. Assuming the ramp is frictionless, compare W1 & W2Work done by gravity is independent of the path!
13 Negative WorkIf some component of the force (Fcosϕ) is in the opposite direction of the displacement, negative work will be done on the objectThis occurs when 90° < ϕ ≤ 180Fϕd
14 Net Work (total Work)If more than one force acts on an object the net work Wnet (aka: total work) is the sum of the work done by each force separately
15 Example 8-4aA car of mass m coasts down a hill inclined at an angle θ below the horizontal. The car is acted on by three forces: the normal force FN exerted by the road, the force due to air resistance Fair, and the force of gravity, mg. Find the total work done on it as it travels a distance d along the road
16 Net Work (total Work)Alternatively, the net work can be calculated by performing a vector sum of all the forces acting on the object to obtain the net force Fnet and then using our basic definition of work
17 Example 8-4bRepeat the calculation in Ex 7-4a using WNET = FNETd cosϕ
18 Kinetic EnergySuppose we have an object accelerating from an initial speed v0 to some new speed v through a distance d, they are related through the eqn:And by Newton’s 2nd Law we know:or
19 Kinetic Energy Combining the two eqns, we have: Multiplying each side by m/2 we have:And recalling that Fnetd = Wnet, we can write:
20 Kinetic EnergyThe quantity ½mv2 is called kinetic energy K, the energy of motionKinetic energy (like work) is a scalarDepends on the speed vHas units of Joules, J
21 Work-Kinetic Energy Theorem Taking K = ½mv2 and K0 = ½mv02 we can write:This is very useful and is known as the Work-Kinetic Energy Theorem
22 Example 8-5A 4.10 kg box of books is lifted vertically from rest a distance of 1.60 m with a constant, upward applied force of 52.7 N. Find the work done by the person lifting it, the work done by gravity, and the final speed of the box.
23 Example 8-6A boy exerts a force of 11.0 N at 29.0° above the horizontal on a 6.40-kg sled. Find the work done by the boy on the sled. Find the final speed of the sled after it moves 2.00 m, assuming the sled starts with an initial speed of m/s and slides horizontally without friction.
24 Graphical Interpretation of Work Work = Area Under the Curve(of a F vs x graph)
26 Graphical Interpretation of Work for a Spring Work = Area Under the Curve(of a F vs x graph)
27 Example 8-7Suppose a block has a mass of 1.5 kg and moves with an initial speed of vi = 2.2 m/s. Find the compression of the spring, whose force constant is 475 N/m, when the block has momentarily come to rest.
28 Power OR Power is the time rate of work How quickly energy is expended Scalar quantityHas SI units of Watts (W) or alt. horsepower (hp)OR
30 Example 8-8To pass a slow-moving truck, you want your fancy 1.30×103-kg car to accelerate from 13.4 m/s (30.0 mi/h) to 17.9 m/s (40.0 mi/h) in 3.00 s. What is the minimum power for this pass?
31 Example 8-10You are driving your 1300-kg car up a 15° incline at a constant speed 29.1 m/s. If the combined resistance (from friction and air resistance) is 650 N. Find the power output of your engine in horespower.