Physics 1611 Remember the Exam Tonight! First exam is Wednesday, February 17, at 6:30 pm in Macbride Auditorium. We will provide an equation sheet (now available on ICON). You should bring a pencil (or two) and a calculator of a type acceptable on the SAT (google calculator SAT to find a list). Do not bring a cell phone. Do not bring your own equation sheet. If you have a conflict and have not arranged a make-up, see me after class!

Topics for Today Work done by gravity (7-3) Proof of relation between work and kinetic energy Work done by a variable force (7-5) Work done by a spring (7-4) Power (7-6) Work Done by Gravity Gravitational force always points downward. Quiz- if an object is traveling downwards in a gravitational field, is the work done

1. Positive 2. Negative Note that gravity is the only force acting on the object. Do Pile Driver Demo Do Demo 1M10.20 - Pile Driver How much energy is required to crush a pop can to half of its original height? 1. 0.5 J 2. 5 J 3. 50 J

4. 500 J Work Done by Gravity How much kinetic energy is gained by a 0.929 kg weight as it drops through a distance of 0.5 meters? 1. Draw diagram with force and displacement 2. What is angle between force and displacement? 3. What is magnitude of force? 4. What is magnitude of displacement? 5. Find 6. Answer

= 0.93 kg 9.8 m/s2 0.5 m = 4.6 kgmm2/s2 = 4.6 J Work and Kinetic Energy Object starts with velocity Is subjected to force acting over distance . Use , find acceleration is So, change in velocity is . Can solve for time, . Position is . Distance traveled is Substitute for t: Work and Kinetic Energy

Have: Multiply by 2a: Have: Recall , so or Work is Define kinetic energy: So Work with Multiple Forces If multiple forces act on an object, then use the net force to calculate the work, just in the same way that you would use the net force to calculate the acceleration.

Work with a Variable Force We have assumed that the force is constant. What about a force that varies as the object moves? We can plot the force as a function of position. Then we can divide up the graph into little pieces Force is roughly constant in each piece. Work = force distance = area of piece. In the limit of very little pieces, we get an integral the work is the integral of

force over position. Work with a Variable Force In symbols, our sum of rectangles is: This becomes the integral:

In three dimensions, we integrate dimension each separately: Spring Force In its relaxed state, a spring produces no force. If the spring is stretched, it tries to pull back to the relaxed state: force is opposite the displacement. If the spring is compressed, it tries to push back to the relaxed state: force is opposite the displacement. Force is given by Hookes law: , where k is the spring that describes how stiff the spring is. Large k means a stiff spring. In one-dimension, we have

Spring Force We can find the work by integrating: Plug -kx in for Fx: Find:

Note that i and f are swapped because of the minus sign in the force law. Work is positive if block ends up closer to the relaxed position (x = 0) and negative if it ends up farther away. Power

Power is the time rate at which a force does work A force does W work in a time t; the average power is: The instantaneous power at a particular time is: The SI unit for power is the watt (W): 1 W = 1 J/s

Therefore work-energy can be written as (power) x (time), for example Watt-seconds or, more commonly, kilowatt-hour. Power Find the instantaneous power using the definition of work:

Where we have used Power is the dot product of force and velocity: Since , we find Power is also the time derivative of (kinetic) energy.

Driving Like James Bond James Bond drives an Aston Martin DB5 that has a mass of 1500 kg and an engine that produces 210 horsepower = 157 kW. How fast can the car accelerate from 0 to 60 mph (97 km/h)? 1. 1 s 2. 3.5 s 3. 8 s 4. 12 s Pulleys

In a single pulley system, if you pull on the rope, the load moves by an equal distance. Also, the force equals the load. Therefore, the work that you do on the rope equals the work that the rope does on the load. Pulleys In a double pulley system, if you pull on the rope, the load moves only half the distance. Quiz - what is the relationship between

the applied force and the load? 1. Force = 0.5 load 2. Force = load 3. Force = 2 load Pulleys Do demo 1M20.11 Pulley systems. Measure weight of load Count number of pulleys What is ratio of pull distance to distance that load moves? What is ratio of load to applied force? Measure applied force, find ratio.

Note that work done is the same. Physics 1611 Remember the Exam Tonight! First exam is Wednesday, February 17, at 6:30 pm in Macbride Auditorium. We will provide an equation sheet (now available on ICON). You should bring a pencil (or two) and a calculator of a type acceptable on the SAT (google calculator SAT to find a list). Do not bring a cell phone. Do not bring your own equation sheet. If you have a conflict and have not arranged a make-up, see me

after class!