1. Physics 218
Lecture 8: Dynamics
Alexei Safonov

2. Free Body Diagrams Same tricks as in Chapters 1-3:
Draw a diagram: Draw each force on an object separately! Force diagram!
Break each force into the X and Y-components, THEN sum!!!
Show your TA that you know the difference between a force, and a component of force
GREAT way to pick up partial credit

3. Closer Look at Elevators
A box of mass m is hung with a string from the ceiling of an elevator that is accelerating upward. Which of the following best describes the tension T in the string:
A) T < mg
B) T = mg
C) T > mg
Lets walk over this step by step a

4. Clicker Question
You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration
A) is upward
B) is downward
C) is zero

5. Clicker Question
You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale.
As you near the top floor and are slowing down, the scale reads
A) More than your usual weight
B) Less than your usual weight
C) Your usual weight

6. If a rope is massless and doesn’t stretch, this means:
Rope Problems
If a rope is massless and doesn’t stretch, this means:
The acceleration of any part of a rope is the same as any other part
The magnitude of the acceleration of the two things it attaches are equal
The tension (Force) exerted by each end is the same

7. Spring Scale
What is the reading in the spring scale?

8. Friction Two types of friction:
Kinetic: The friction force that slows things down
Static: The force that makes it hard to even get things moving

9. Refrigerator
If you push a refrigerator when there is no friction what happens?
In the real world what happens? Especially when it’s fully loaded and on a sticky kitchen floor?
When does static friction kick in?
When does kinetic friction kick in?

10. FFriction = mKineticFNormal
Kinetic Friction
For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write
FFriction = mKineticFNormal
Here m is a constant
Warning:
THIS IS NOT A VECTOR EQUATION!

11. FFriction  mStaticFNormal
Static Friction
This is more complicated
For static friction, the friction force can vary
FFriction  mStaticFNormal
Example of the refrigerator:
If I don’t push, what is the static friction force?
What if I push a little?

12. Friction Only appears if there is a force trying to move an object
If force is applied, but object is not yet moving: Static Friction.
Friction is EQUAL to the force
Friction can’t grow beyond mN, so when external force gets big enough, motion starts – Kinetic Friction.
Always equal to mN

13. Problem Solving
Most problems are in the intersection of Kinematics and Dynamics. Useful tips:
If the motion is specified (e.g. “at rest”, “constant speed”, “uniform circular”), that is important information. Use it to get the net force (e.g. from the acceleration value)
You don’t yet know where it is from, but you know it got to be there!
Separately calculate forces acting on the object
Connect the two pieces of information and solve for the unknowns

14. Pulling a Box
What is the magnitude of the static frictional force acting on the box? Mg
mMg T

15. Pulling a Box
What is the magnitude of the static frictional force acting on the box? Mg
mMg T

16. Two Boxes and a Pulley
You hold two boxes, m1 and m2, connected by a rope running over a pulley at rest. The coefficient of kinetic friction between the table and box I is m. You then let go and the mass m2 is so large that the system accelerates
Q: What is the magnitude of the acceleration of the system?
Ignore the mass of the pulley and rope and any friction associated with the pulley

17. In which case is the tension in the string the biggest?
Same

18. In which case is the tension in the string the biggest?
Same in both

19. Is it better to push or pull a sled?
You can pull or push a sled with the same force magnitude, FP, but different angles Q, as shown in the figures.
Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, m, which is better? FP

20. You push a crate from the back of an elevator to the front (with friction). Which requires the least force?
Elevator is moving up with constant speed.
Elevator is moving down with constant speed.
Elevator is accelerating upwards.
Elevator is accelerating downwards.
All require the same force.

21. Acceleration & Friction
Which of the following diagrams best describes the static frictional force acting on the box?

22. Acceleration & Friction
Which of the following diagrams best describes the static frictional force acting on the box?

23. Box on an inclined plane 2
A box has non-negligible friction with the surface and the coefficient of friction is m. The inclined plane is adjustable and we change q from 0 to 90 degrees. Mass is known and is equal to m. Calculate and draw a graph of:
How does the friction force depend on q
Acceleration ? q

24. Circular Motion, centripetal acceleration and force
1) Objects moving in a circle always have a component of acceleration, called centripetal, which is toward the center of the circle.*
2) Centripetal acceleration must be caused by a force:
Friction, gravity – whatever force keeps it moving in a circle.
This force is often called the “centripetal force”
3) There is no “new” kind of force here.
4) There is no such thing as centrifugal force.
* They can have also have tangential acceleration if their speed is not constant

25. Banking Angle
You are a driver on the NASCAR circuit. Your car has m and is traveling with a speed V around a curve with Radius R
What angle, Q, should the road be banked so that no friction is required?

26. Problems with Circular Motion
Most of these problems are solved by:
Considering kinematics (centripetal acceleration) which yields the resultant force
It’s not a real force really, you are basically “guessing” the answer for how the real forces must have added up to allow the kind of motion that happens here
Be careful with the direction of acceleration!
Step back and look at real forces
You already know how they must have added up, now your task is to see how that can happen
Bring the two pieces of the puzzle together and find what they are asking about

27. Other tricks What is minimum velocity for the car not to fall down?
Radius, mass are given
Key question: how do you identify the critical moment when something happens that makes the car fall?
Normal force!
How about a problem with a ball on a string that you rotate in vertical plane with constant speed and you want it to swing without sagging at the top?
What force should you look at?

28. Conical Pendulum
A small ball of mass m is suspended by a cord of length L and revolves in a circle with a radius given by r = LsinQ.
What is the velocity of the ball?
Tension FT?
Calculate the period of the ball.

29. An Incline, a Pulley and two Boxes
In the diagram given, m1 and m2 remain at rest and the angle Q is known. The coefficient of static friction is m and m1 is known.
What is the mass m2?
Is it a single value or a range?
Ignore the mass of the pulley and cord and any friction associated with the pulley m2 m1 Q