1. Chapter 5 Applications of Newton’s Law

2. 2d equilibrium
Find the tensions in terms of the mass m of the engine.

3. Tension

4. Static friction vs Kinetic friction

5. Static Friction
Kinetic friction is the friction when the object is moving. Static friction is when it is at rest.

6. Example: Incline
It is found that the object starts sliding once the angle θ becomes greater than θc.
Find μs in terms of θc.

7. Kinetic Friction (more useful)
Kinetic friction is the friction when the object is moving. Static friction is when it is at rest.

8. Example
Find the horizontal acceleration of the box of 3kg on a surface given μk = 0.5 and F = 20N.

9. Pulling a crate
Given mg =500N and μk=0.4. How hard do you have to pull to keep the crate moving at constant velocity?

10. Solution

11. The Sliding Crate
Find the acceleration given θ =30°, μk=0.192.

12. Centripetal force and acceleration
According to Newton’s Laws, anything that is not moving in a straight line must have a net force acting on it and must be accelerating.
When an object is moving in a circle, there must be a net force, causing the “centripetal acceleration”.
Even though the speed of the object is constant, the velocity is constantly changing because of the changing direction. That is why the acceleration is non-zero. r v x y
(x,y)

13. Centripetal force and acceleration

14. Must remember this:
Using this you can convert freely among ω, T, f and v.

15. Centripetal force and acceleration

16. Centripetal force and acceleration
Centripetal force is the force required to keep an object in circular motion. Without it the object will resume moving in a straight line.
In this case, the centripetal force is the tension in the string.

17. How fast can it spin?
The cord breaks when tension is greater than 50N. Given m=0.5kg, r =1.5m, how fast can it spin?
In this case, the centripetal force is the tension in the string.
What is the tension when v =7m/s?

18. Examples of centripetal force

19. Gravity as centripetal force
In this case, the gravitational force (i.e. the weight) is the centripetal force.
However, you must remember that in outer space, g <9.8m/s2!!!
The value of g (acceleration under free fall) is usually given, and you will also learn how to calculate it in Chapter 13.

20. What you have learned Static and kinetic friction
Centripetal force and acceleration