3/18 do now – on a new sheet1. A negatively charged rod is brought near a neutral object

without touching it. The overall charge on the object will become

a) neutral b) positive c) negative

2. A negatively charged rod is used to charge a neutral object by induction. The overall charge on the object will become

a) neutral b) positive c) negative

12.1 – simple harmonic motion

1. Identify the conditions of simple harmonic motion

2. Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.

3. Calculate the spring force using Hooke’s law.

Homework – Due 12.1 reading questionsCastle learning Chapter 12.2 reading questions – due Thursday 3/20/14Chapter 12 Project – due Monday 3/31/14Chapter 12 Test – Tuesday 4/1/14

What is simple harmonic motion?

• SHM is a vibration about an equilibrium position in which a RESTORING FORCE IS PROPORTIONAL TO THE DISPLACEMENT FROM EQUILIBRIUM.

kxF

mgF

• The restoring force is the force of the spring

The restoring force is the force weight of the bob

force, velocity, and acceleration • At equilibrium:

– Force is ZERO – (Mg = kX)– Acceleration is ZERO (a = F/M)– Velocity is MAXIMUM

• At maximum displacement:– Force is MAXIMUM– Acceleration is MAXIMUM (a=F/M)– Velocity is ZERO

Hooke’s Law• In most mass-spring systems, the restoring force exerted on

the mass by a spring is in the opposite direction as the displacement, its magnitude is directly proportional to the displacement of the mass stretched or compressed from its equilibrium position.

kxFelastic

• F is the force on the spring (N)• k is the spring constant (N/m)• x is the displacement from equilibrium (m)

Hooke’s Law

Hooke’s Law applies to THISregion ONLY!

• A spring with a spring constant of 10 newtons per meter is stretched 0.5 meter. What force must be applied to the spring?

FS = kx

FS = (10 N/m)(0.5 m)

FS = 5.0 N

Example #1

• What is the spring constant of an elastic object if it stretches 2.0 centimeters when pulled with a force of 30 newtons?

FS = kx k = FS / x

k = (30 N)/(0.02 m)

k = 1500 N/m

Example #2

A stretched or compressed spring has potential energy

2

21 kxPEelastic

• At equilibrium position, PEelastic is zero.• At maximum displacement, PEelastic is

maximum

Example #3• A 20.-newton weight is attached to a spring,

causing it to stretch, as shown in the diagram.a. What is the spring constant of this spring?b. What is the potential energy is stored in the

spring?

1. The motion of Earth orbiting the sun is periodic. Is this motion simple harmonic? Why or why not?

2. In a pinball games, the force exerted by a compressed spring is used to release a ball, if the distance the spring is compressed is doubled, how will the force acting on the ball change? If the spring is replaced with one that is half as stiff, how will the force acting on the ball change?

Questions

Class work – answer on a sheet of paper, with today’s date

1. What distance will a spring with a spring constant of 1200 newtons per meter stretch when a force of 50 newtons is applied to it?

2. What does the slope of the graph below represent? How do you know that the graph represents data taken for an object that does obey Hooke’s Law?

3. How much force is needed to stretch a spring with a spring constant of 1000 newtons per meter a distance of 0.04 meter? [40N]

4. What is the spring constant of a spring that is compressed a distance of 0.06 meter when pushed with a force of 50 newtons? [833N/m]

5. What distance will a spring with a spring constant of 600 newtons per meter be stretched when a force of 3.0 x 102 newtons is applied? [0.5 m]

7.

6.

8. A pendulum bob is pulled back to position A and released from rest. The bob swings through its usual circular arc and is caught at position C. Determine the position (A, B, C or all the same) where the …

a. force of gravity is the greatest.b. restoring force is the greatest.c. speed is the greatest.d. potential energy is the greatest e. kinetic energy is the greatest.f. total mechanical energy is the greatest.

Lab 17 – Resistors in parallel