Physics 151 Week 12 Day 1 Topics: Energy, Power, Hooke’s Law, and Oscillations (Chs. 8, 10, & 14)  Energy  Work-Energy Theorem  Similar to Constant a equation without time  Example Problems  Power  Springs  Hooke’s Law  Applications  Oscillations  Period & Frequency

Work Energy Theorem Slide W net =  ma*Delta x * cos(  )= 1/2 mv f 2 - 1/2 mv i 2 2 * ma*Delta x = 2 * (1/2 mv f 2 - 1/2 mv i 2 ) v f 2 - v i 2 = 2a*Delta x v f 2 = v i 2 + 2a*Delta x Look familiar?

Work Energy Problem 2 Slide A 1000 kg car is rolling slowly across a level surface at 1 m/s, heading towards a group of small children. The doors are locked so you can't get inside and use the brake. Instead, you run in front of the car and push on the hood at an angle 30 degrees below the horizontal. How hard must you push to stop the car in a distance of 1 m?

Work Energy Problem 1 Slide A 1 kg block moves along the x-axis. It passes x = 0 with a velocity v = 2 m/s. It is then subjected to the force shown in the graph below. a.Which of the following is true: The block gets to x = 5 m with a speed greater than, less than, or equal to 2 m/s. State explicitly if the block never reaches x = 5 m. b.Calculate the block speed at x = 5 m.

A typical human head has a mass of 5.0 kg. If the head is moving at some speed and strikes a fixed surface, it will come to rest. A helmet can help protect against injury; the foam in the helmet allows the head to come to rest over a longer distance, reducing the force on the head. The foam in helmets is generally designed to fail at a certain large force below the threshold of damage to the head. If this force is exceeded, the foam begins to compress. If the foam in a helmet compresses by 1.5 cm under a force of 2500 N (below the threshold for damage to the head), what is the maximum speed the head could have on impact? Use energy concepts to solve this problem. Example Problem Slide 10-46

Power Same mass... Both reach 60 mph... Same final kinetic energy, but different times mean different powers. Slide 10-40

Power Slide Instantaneous Power

Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power? CarMass (g)Speed (m/s)Time (s) A10032 B20022 C 23 D30023 E 14 Checking Understanding Slide 10-41

Answer Four toy cars accelerate from rest to their top speed in a certain amount of time. The masses of the cars, the final speeds, and the time to reach this speed are noted in the table. Which car has the greatest power? CarMass (g)Speed (m/s)Time (s) A10032 B20022 C 23 D30023 E 14 Slide 10-42

Data for one stage of the 2004 Tour de France show that Lance Armstrong’s average speed was 15 m/s, and that keeping Lance and his bike moving at this zippy pace required a power of 450 W. A.What was the average forward force keeping Lance and his bike moving forward? B.To put this in perspective, compute what mass would have this weight. Example Problem Slide 10-47

The Spring Force The magnitude of the spring force is proportional to the displacement of its end: F sp = k ∆l Slide 8-21

The spring force is directed oppositely to the displacement. We can then write Hooke’s law as Hooke’s Law (F sp ) x = –k ∆x Slide 8-22

Equilibrium and Oscillation Slide 14-12

Frequency and Period Period The time  t for the oscillator to make one complete cycle Frequency The number of cycles in a given amount of time. For example: the number of cycles per second (units => Hertz - Hz )

Linear Restoring Forces and Simple Harmonic Motion Slide 14-13

Sinusoidal Relationships Slide 14-21