Lecture 6. Analytical Physics 123 Prof. Noronha-Hostler Prof. Montalvo. Oct 12 th, 2018

Transcription

1 Lecture 6 Analytical Physics 123 Prof. Noronha-Hostler Prof. Montalvo Oct 12 th, 2018

2 Tests The average was lower than expected, will discuss with Prof. Montolvo about a curve. Grades probably posted after classes are done. Don t be discouraged, still possible to come back from a low grae!

3 Objectives Apply Newton s laws Draw Free body diagrams Solve for acceleration, tension etc.

4 Sliding block (free body diagrams) Assume that the table is frictionless.. This helps so we can ignore the frictional force for now. Assume the pulley is massless This helps so we can ignore rotation (next semester)

5 Sliding block First, let s focus on Mass 1 F N

6 Sliding block First, let s focus on Mass 1 Direction x F N T x =m 1 a x Direction y F N -F g =0 F N =F g =m 1 g

7 Sliding block Next, let s focus on Mass 2

8 Sliding block Next, let s focus on Mass 2 Direction x No forces Direction y T-F g =-m 2 a T-m 2 g=-m 2 a

9 Solving for tension and acceleration Collecting all the equations T-m 2 g=-m 2 a T=m 1 a F N =m 1 g We now have three equations and two unknowns (T and a). Which equation can we ignore?

10 Solving for tension and acceleration Collecting all the equations T-m 2 g=-m 2 a T=m 1 a F N =m 1 g Which equation can we ignore? This is for the y direction for the block on the table. It s not moving vertically, so it doesn t help us find T or a.

11 What is the tension? T-m 2 g=-m 2 a a=-(t-m 2 g)/m 2 Recall T=m 1 a, substitute in a T=-m 1 (T-m 2 g)/m 2, solve for T m 2 T+m 1 T=m 1 m 2 g T=m 1 m 2 g/(m 2 +m 1 )

12 What is the acceleration? T=m 1 a and T=m 1 m 2 g/(m 2 +m 1 ) m 1 a=m 1 m 2 g/(m 2 +m 1 ) a=m 2 g/(m 2 +m 1 )

13 What if there was friction on m 1? f F N

14 What if there was friction on m 1? T-f=m 1 a f F N Note, only if T>f will the block move! Demo on red block pulling

15 What if a block is on inclined plane?

16 x direction

17 y direction Block is NOT accelerating in the y direction (smart choice of axes!!!)

18 And then we add a pulley+block

19 Collect the equations What if they are in equilibrium? T=m (g-a) T-mg sin(θ)=ma a=0 T=m g T-mg sin(θ)=0 T=mg sin(θ) m =m sin(θ)

20 What if m=1000 g (Demo)? m =m sin(θ) 1000g =1000g sin(30) =500 g =30 0

21 How much is the normal force? F y =mg sin(θ) 1000g =1000g*9.8m/s 2 cos(30) = g*m/s 2 =30 0

22 Can we replicate the normal force? F y = g*m/s 2 =T 1000g T=m g m =866g =30 0

23 Blocks pushing each other F app Mass A Mass B What is the force of block B on block A?

24 Free body diagram of Mass B F app Mass A F AB F app -F AB =m A a

25 Free body diagram of Mass B F BA Mass B F BA =m B a

26 Collecting the equations F app -F AB =m A a and F BA =m B a F app =m A a+m B a=(m A +m B )a If the applied force is F app =20N and the mass A is m A =2kg and mass B is m B =8 kg, what is the acceleration? a=f ap /(m A +m B ) =20 N/(2kg+8kg) =2 m/s 2

27 Collecting the equations If the applied force is F app =20N and the mass A is m A =2kg and mass B is m B =8 kg, what are the contact forces of each book on each other? a=2 m/s 2 F app -F AB =m A a F AB =F app -m A a =20N-2kg*2 m/s 2 F AB =16N F BA =m B a =8kg*2 m/s 2 F BA =16N The contact forces are equal! F AB =F BA

28 Two types of friction Static frictional force fs Kinetic frictional force fk f s a=0 Pulling force Here the block doesn t move because it can t overcome the static frictional force! When the block accelerates, the resistance to movement is f k v>0 f Pulling force k

29 Two Types of friction Static frictional force fs 1. a=0, then f s =F pull (parallel to surface) 2. Maximum value f s,max =μ s F N Kinetic frictional force fk Coefficient of state friction 3. a>0, the frictional forces to f k such that f k =μ k F N Coefficient of kinetic friction

30 Surfaces and coefficient of friction Recall f s,max =μ s F N and f k =μ k F N How does the mass of the block affect its frictional force? (a)increasing mass, decreases the frictional force (b)decreasing mass, decreases the frictional force (c)the mass plays no role in friction (d)doubling the mass, triples the frictional force (e)doubling the mass, reduces the frictional force by a third. f Pulling force

31 When will the sandpaper side slip? a) Any angle b) It will never slip c) It will slip at a smaller angle than the other side d) It will slip at a larger angle than the other side e) Not enough information

32 Can these phone books be pulled apart? (a) Yes they will ALWAYS be pulled apart (b) No, never, it s impossible (c) Only someone/something really strong (d) I need a nap (e) Yes, if you remove the secret tape between the different layes

33 Car demo

34 Stopping distance for a car x-x 0 μ=0.60 v=0 v 0 Since the car is moving, we calculate the kinetic friction fk Substituting in F N =mg, Then, a=-μ f k =μ k F N =ma k g

35 Stopping distance for a car x-x 0 μ=0.60 v=0 Since the acceleration is constant, we can use v 2 =v 02 +2a(x-x 0 ) x-x 0 =(v 2 -v 02 )/(2a)=-(v 2 -v 02 )/(2μ k g) v 0 Recall a=-μ k g

36 Stopping distance for a car x-x 0 μ=0.60 v=0 x-x 0 =-(v 2 -v 02 )/(2μ k g) If v 0 =10 m/s and v=0 m/s, then x-x 0 ~8.5 m v 0 Recall a=-μ k g

37 And on ice? μ=0.10 x-x 0 v=0 v 0 x-x 0 =-(v 2 -v 02 )/(2μ k g) If v 0 =10 m/s and v=0 m/s, then x-x 0 ~51 m

38 Next week Drag force Uniform circular motion More on friction