Power. Power is the rate at which energy is transformed from one type to another: Average power: Power is a scalar quantity. Unit:

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1 Power Power is the rate at which energy is transformed from one type to another: Average power: Power is a scalar quantity. Unit: Alternative expression for power: if F is parallel to Δx.

2 Example problem: Power A shot-putter accelerates a 7.3-kg shot from rest to 14 m/s. If this motion takes 2.0 s, what average power was produced?

3 Horsepower - An alternative unit of Power When James Watt invented the steam engine, he needed a large power unit to rate the output power of his new invention. He chose a standard horse.

4 Kilowatt-hour: A unit of energy When you read your electricity bill, it will tell you how many kilowatt-hours (KWHRS, kwh) you consumed. What does that mean? 1 kwh is the energy consumed in 1 hour at the constant rate of 1 kw. kwh is a unit of energy, not power!

5 Get a feeling for the value of energy How many hamsters running on wheels would it take to provide enough power for a house? Let's assume a hamster weighing 50 grams can run up a 30-degree slope at 2 m/s. 120 hamsters to keep a 60-watt bulb lit Average hamster probably spends ~5 % of its life running, so we would need 2,400 hamsters just for lightbulb The average household needs a constant power consumption of about ~2.5 kw. Each house would need ~100,000 hamsters.

6 Review If non-conservative forces can be neglected, the sum of potential and kinetic energy will be conserved. Typical problems that can be solved by energy conservation: Rollercoasters, Pendulums, Jumping. Power is defined as the rate of energy transfer with time (scalar quantity): Unit: 1 W = 1 J/s 1 horsepower is an alternative unit for power (non SI-unit): 1 hp = 746 W 1 kilowatt-hour is a unit for energy. It is the energy consumed within 1 hour at the rate of 1 W:

7 Example problem: Horsepower An advertisement claims that a certain 1200 kg car can accelerate from rest to a speed of 25 m/s in a time of 8.0 s. What power (in units of horsepower) must the motor produce in order to cause this acceleration? Ignore losses due to friction. (1 hp=746 W)

8 Example problem: Cost of Energy What is the cost of forgetting to turn off your bathroom light for the day? Let s say you have three 75W bulbs in this light and you are gone for 12 hours. Electricity costs about $0.10 per kwh.

9 Example problem: Conservation of energy A rollercoaster car is at the top of a hill. If its speed at the top of the hill is 2.0 m/s, calculate the speed ignoring friction at the point P shown below: P 50.0 m 30.0 m

10 Fun Example: The Flash The Flash runs so fast that he can pluck bullets from the air (Flash s speed > speed of bullets). Where does all of this energy come from? - Food. The Flash eats for the same reason we do. Let s calculate how much Flash must eat in order to be able to run so fast.

11 How much does the Flash have to eat? KE = 1 mv The Flash s (and our) caloric intake requirements increase quadratically the faster we run. Twice as fast means four times the calories needed to fuel the running. Let s say Flash s mass is 70 kg (155 pounds) and he is running at 1 % the speed of light (v = m/s). 2 2 How many calories is this? - 1 calorie = 4184 J. That s about 150 million burgers! KE = 75 billion calories!

12 Example problem: Springs A spring attached to a wall has a spring constant (k) of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. (a) Find the energy stored in the spring when the mass is compressed 6.00 cm from equilibrium. (b) Write the conservation of energy equation and solve it for the speed of the mass as it passes equilibrium. (c) What is the speed at the halfway point?

13 Example problem: Power A bicyclist coasts down a 7.0 o hill at a steady speed of 5.0 m/s. Assuming a total mass of 75 kg (bicycle plus rider). What must be the cyclist s power output to climb the same hill at the same speed?