1. An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true?
a) The work done by the tension force is zero joules.
b) The net work done by the two forces is zero joules.
c) The work done by the gravitational force is zero joules.
d) The magnitude of the work done by the gravitational force is larger than that done by the tension force.
e) The magnitude of the work done by the tension force is larger than that done by the gravitational force.

2. 6. 3. 5. Consider the box in the drawing
Consider the box in the drawing. We can slide the box up the frictionless incline from point A and to point C or we can slide it along the frictionless horizontal surface from point A to point B and then lift it to point C. How does the work done on the box along path A-C,WAC, compare to the work done on the box along the two step path A-B-C, WABC?
a) WABC is much greater than WAC.
b) WABC is slightly greater than WAC.
c) WABC is much less than WAC.
d) WABC is slight less than WAC.
e) The work done in both cases is the same.

3. Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice the mass of the other. When the balls reach the ground, how do the kinetic energies of the two balls compare?
a) The lighter one has one fourth as much kinetic energy as the other does.
b) The lighter one has one half as much kinetic energy as the other does.
c) The lighter one has the same kinetic energy as the other does.
d) The lighter one has twice as much kinetic energy as the other does.
e) The lighter one has four times as much kinetic energy as the other does.

4. A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. By which one of the following means can the centripetal acceleration of the ball be increased by a factor of two?
a) Keep the radius fixed and increase the period by a factor of two.
b) Keep the radius fixed and decrease the period by a factor of two.
c) Keep the speed fixed and increase the radius by a factor of two.
d) Keep the speed fixed and decrease the radius by a factor of two.
e) Keep the radius fixed and increase the speed by a factor of two.

5. A ball is attached to a string and whirled in a horizontal circle. The ball is moving in uniform circular motion when the string separates from the ball (the knot wasn’t very tight). Which one of the following statements best describes the subsequent motion of the ball?
a) The ball immediately flies in the direction radially outward from the center of the circular path the ball had been following.
b) The ball continues to follow the circular path for a short time, but then it gradually falls away.
c) The ball gradually curves away from the circular path it had been following.
d) The ball immediately follows a linear path away from, but not tangent to the circular path it had been following.
e) The ball immediately follows a line that is tangent to the circular path the ball had been following

6. Imagine you are swinging a bucket by the handle around in a circle that is nearly level with the ground (a horizontal circle). What is the force, the physical force, holding the bucket in a circular path?
a) the centripetal force
b) the centrifugal force
c) your hand on the handle
d) gravitational force
e) None of the above are correct.

7. Oscillatory motion (non-constant acceleration)
Simple Harmonic Motion

8. 10.1 The Ideal Spring and Simple Harmonic Motion
spring constant
Units: N/m

9. 10.1 The Ideal Spring and Simple Harmonic Motion
HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING
The restoring force on an ideal spring is

10. 10.2 Simple Harmonic Motion and the Reference Circle
file:///Users/silvinagatica/Desktop/simulations/applets/sim08.htm
amplitude A: the maximum displacement
period T: the time required to complete one cycle
frequency f: the number of cycles per second (measured in Hz)

11. 10.2 Simple Harmonic Motion and the Reference Circle
DISPLACEMENT
VELOCITY
ACCELERATION

12. 10.2 Simple Harmonic Motion and the Reference Circle
FREQUENCY OF VIBRATION

13. 10.2 Simple Harmonic Motion and the Reference Circle
Example 6 A Body Mass Measurement Device
The device consists of a spring-mounted chair in which the astronaut
sits. The spring has a spring constant of 606 N/m and the mass of
the chair is 12.0 kg. The measured
period is 2.41 s. Find the mass of the
astronaut.

14. 10.2 Simple Harmonic Motion and the Reference Circle

15. 10.3 Energy and Simple Harmonic Motion
F=-kx F
Work=Area = x0 xf x
-kx0
-kxf

16. 10.3 Energy and Simple Harmonic Motion
DEFINITION OF ELASTIC POTENTIAL ENERGY
The elastic potential energy is the energy that a spring
has by virtue of being stretched or compressed. For an
ideal spring, the elastic potential energy is
SI Unit of Elastic Potential Energy: joule (J)

17. 10.3 Energy and Simple Harmonic Motion
simulation

18. 10.2 Simple Harmonic Motion and the Reference Circle
SUMMARY:
Period T: time when ωt = 2 π
Frequency f: # cycles per second
ω: angular frequency (how fast it ocillates)
simulation horizontal oscilator

19. A simple pendulum consists of a particle attached to a frictionless
10.4 The Pendulum
A simple pendulum consists of
a particle attached to a frictionless
pivot by a cable of negligible mass.
Does T depend on the mass?
simulation

20. A simple pendulum consists of a particle attached to a frictionless
10.4 The Pendulum
A simple pendulum consists of
a particle attached to a frictionless
pivot by a cable of negligible mass.
How much would you change L to double T?
simulation

21. Determine the length of a simple pendulum that will
10.4 The Pendulum
Example 10 Keeping Time
Determine the length of a simple pendulum that will
swing back and forth in simple harmonic motion with
a period of 1.00 s.

22. 10.1 The Ideal Spring and Simple Harmonic Motion
Example 1 A Tire Pressure Gauge
The spring constant of the spring
is 320 N/m and the bar indicator
extends 2.0 cm. What force does the
air in the tire apply to the spring?

23. 10.1 The Ideal Spring and Simple Harmonic Motion

24. 10.5 Damped Harmonic Motion
In simple harmonic motion, an object oscillated
with a constant amplitude.
In reality, friction or some other energy
dissipating mechanism is always present
and the amplitude decreases as time
passes.
This is referred to as damped harmonic
motion.

25. 10.5 Damped Harmonic Motion
simple harmonic motion
2&3) underdamped
critically damped
5) overdamped

26. 10.6 Driven Harmonic Motion and Resonance
When a force is applied to an oscillating system at all times,
the result is driven harmonic motion.
Here, the driving force has the same frequency as the
spring system and always points in the direction of the
object’s velocity.

27. 10.6 Driven Harmonic Motion and Resonance
Resonance is the condition in which a time-dependent force can transmit
large amounts of energy to an oscillating object, leading to a large amplitude
motion.
Resonance occurs when the frequency of the force matches a natural
frequency at which the object will oscillate.