Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 2

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1 Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 1 3 problems from exam 2 6 problems (including 14.5) 8 problems Go through the homework, discussion and clicker quizzes problems carefully.

2 HITT RF Remote Login Procedure: The radio channel number for this room is 07 (zero, seven). It is STRONGLY recommended to login your remote for every class just to be sure it is on the correct radio channel and working before class. 1. PRESS AND HOLD THE DOWN ARROW KEY until the GREEN light on the remote turns RED. 2. PRESS THE 0 KEY and you will see the RED light flash GREEN. 3. PRESS THE 7 KEY and you will see the RED light flash GREEN. 4. PRESS AND RELEASE THE DOWN ARROW KEY again and you will see the red light search for the receiver, if it BLINKS GREEN MULTIPLE TIMES you are logged in.

3 Ch Ch. 3 Units: Look what is given, convert all numbers to SI units, then substitute in your final formula! Vectors: (Scalars vs Vectors) Addition Subtraction

4 Linear Motion with const. a Displacement vs. distance Velocity vs. speed Average velocity vs. average speed Kinematic Equations v = v + at o o x = v t + 1 at v = v + 2a x x = v average o 2 vo + v t = 2 f t

5 Projectile motion x- uniform motion y- constant acceleration Relative Velocity: v r = v r v r AB AE EB

6 Example Car moving at 25 m/s hits the brakes & stops in a distance of 25 m What was the car s (uniform) acceleration? A m/s 2 B m/s 2 C. 1.0 m/s 2 D. 50 m/s 2 E. -50 m/s 2 How long did it take to stop?

7 Example A ball is launched straight upward with an initial speed of 20 m/s. How long does it take to return? A. 10 s B. 8 s C. 6 s D. 4 s E. 2 s How high did it go?

8 How far before the plane gets to the hikers does the rescuer need to drop the parcel? A. 180 m B. 150 m C. 120 m D. 100 m E. 50 m 125 m 30 m/s

9 Ch. 4 Newton s Laws Force Vector Add forces 1 st law 2 nd law 3 rd law Equilibrium Friction r r r r F = F + F + F +... net r F = ma r net Free-body Diagram!!

10 Example Woman pulls 75 kg sled at an angle 42 with constant velocity along a flat road. (µk=0.1) What is the tension in the pulling rope? m T Ground

11 Example Block being pulled up a hill. What tension must rope have before block moves? (m=10kg, θ=25, µs=0.6) y max f s n T x y T x mg θ

12 Ch. 5 Work and Energy Work KE PE W-KE Theorem Conservation WE theorem Power W (Fcos θ) x Wnet = KEf KEi = KE KE + PE = KE + PE i i f f W = ( KE KE) nc f i + ( PE PE) = 0 f i

13 76. A 2.00-kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m (Fig. P5.76). The block is released from rest when the spring is unstretched, and the pulley is frictionless. The block moves 20.0 cm down the incline before coming to rest. Find the coefficient of kinetic friction between block and incline. A B C D

15 The launching mechanism of a toy gun consists of a Hooke s law spring of unknown spring constant. If the spring is compressed a distance of m and the gun fired vertically, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, determine the spring constant N/m N/m N/m N/m

16 W nc = KE + PE g + PE s W nc = 0 KE = 0 PE g = - PE s PE gf PE gi = PE si PE sf mgh = (1/2)kx 2 k = (2mgh)/x 2

17 Ch. 6 Momentum, M. Cons. r r p = mv Momentum Impulse Impulse momentum theorem Conservation collisions r I = F t Ft = = p r F( t 2 t1) = p p f i

18 A 20-kg object sitting at rest is struck in a head-on collision with a 10-kg object initially moving at +5.0 m/s. If the 10- kg object moving at +1.0 m/s after the collision. Find the velocity of the 20-kg object after the collision. a m/s b m/s c m/s d m/s

19 An 8.00 g bullet is fired into a 280 g block that is initially at rest at the edge of a table of 1.00 m height. The bullet remains in the block, and after the impact the block lands d = 2.1 m from the bottom of the table. Determine the initial speed of the bullet. A m/s B m/s C m/s D. 166 m/s Scanned solutions 2

20 Linear vs Rotation Linear Motion coordinate x velocity v acceleration a θ ω α Rotational Motion angle angular velocity angular acceleration mass m force F 1 st Newton s Law F=0: v=const 2 nd Newton s Law F = ma Ι τ τ=0: ω=const τ = Iα moment of inertia torque Kinetic Energy KE = ½mv 2 Momentum p = mv KE = ½Iω 2 Kinetic Energy L= Iω Angular Momentum

21 Analogies Between Linear and Rotational Motion Relations between angular and linear quantities s a = r θ; = rα; v t a c t = rω = v r 2 2 = rω

22 The planet is rotating about the vertical axis with constant angular velocity ω. What is the acceleration of the mass m at point A. R A A. 0 B m B. g C. ω 2 R

23 The planet is rotating about the vertical axis with constant angular velocity ω. What is the acceleration of the mass m at point B. R A A. 0 B m B. g C. ω 2 R

24 Part of a roller-coaster ride involves coasting down an incline and entering a loop 8.00 m in diameter. For safety considerations, the roller coaster's speed at the top of the loop must be such that the force of the seat on a rider is equal in magnitude to the rider's weight. From what height above the bottom of the loop must the roller coaster descend to satisfy this requirement? A.12.0 m B m C m D.100 m Scanned solutions 3

25 A wheel undergoes constant angular acceleration. Find the angular acceleration if the initial angular velocity is zero and the final angular velocity after 10 s is 100 rad/s. A.1 rad/s 2 B.10 rad/s 2 C.100 rad/s 2 ω f = ω i + αt 100 = α D.1000 rad/s 2

26 1. Choose origin P 2. Find distance of the point P (where the force is being applied to the beam) from the origin O. This is the value of r. θ F Fsinθ 3. Find the angle θ the force F makes with the beam i.e. think of the beam as the x-axis. O 4. Find the component of the force F which is perpendicular to the beam i.e. think of the beam as the x-axis and find the y-component of F which is Fsinθ.

27 5. Torque τ = r F sin θ P θ Fsinθ 6. If the force F is tending to rotate the beam clockwise then τ is negative. F O

28 A 100-N uniform ladder rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is What minimum angle can the ladder make with the floor before it slips? A. 42 o B. 22 o C. 18 o D. 51 o E. 39 o

29 Example: a ladder against a wall What minimum angle can the ladder make with the floor before it slips? P x F = 0 f s P = 0 F y = 0 n mg = 0 τ = 0 L PLsin θ mg sin(90 θ ) = 2 fs = µ sn = µ smg y 0 x N θ f s mg L µ s mglsin θ mg cosθ = 0 µ s sinθ cosθ = 0 1 tan θ = 2µ s

30 Rolling down incline Energy conservation Linear velocity and angular speed are related v=rω 1 mgh = mv Iω mgh = mv + ( ) v = ( m (1 I gh = + ) v 2 2 mr Smaller I/mR 2, bigger v, faster!! 1 2 I R 2 h I R 2 ) v 2 v

31 Example ω i ω f

32 Example: solution

33 Example, cont. a. How much work was done by the elephant if the radius of the carousel is 2 m? b. How much work was done to the elephant? c. How much work was done to the carousel?

The puck has a mass of 0.129 kg. Its original distance from the center of rotation is 0.4 m and it moves with a speed of 0.8 m/s.

34 The puck has a mass of kg. Its original distance from the center of rotation is 0.4 m and it moves with a speed of 0.8 m/s. The string is pulled downward 0.15 m through the hole in the frictionless table. Determine the work done on the puck. What is the angular momentum of the puck?

35 A sample of blood is placed in a centrifuge of radius 13.0 cm. The mass of a red blood cell is 3.0 X kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 X N. At how many revolutions per second should the centrifuge be operated? 161 rev/s

36 The Earth has a radius of about 6400 km. At what altitude is the acceleration of gravity about 1/9 that of g (acceleration of gravity at the surface of the Earth = 9.8 m/s 2 )? A km B km C km D km E. 12,800 km g = G ME r 2 M E = kg G = x N m² /kg² Gravitational force from multiple masses

37 The Earth has a radius of about 6400 km. If an object is dropped from 12,800 km above Earth s surface, what is its speed when it hits Earth s surface? A. 1 km/s B. 3 km/s C. 6 km/s D. 9 km/s E km/s PE g M Em = G r M E = kg G = x N m² /kg²

38 Ch. 9 Solid and Fluid Elastic Modulus Fluid Pressure Pascal s Principle Archimedes Principle

39. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density = 7.

39 39. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density = kg/m 3 )is suspended from a spring scale and is completely submerged in the oil (Fig. P9.39). Find the equilibrium readings of both scales.

40 43. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density = kg/m 3 )is suspended from a spring scale and is completely submerged in the oil (Fig. P9.39). Find the equilibrium readings of both scales. Will the reading of the upper scale be 1. Less than weight of iron 2. Greater than weight of iron 3. Equal to weight of iron

43. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density = 7.

41 43. A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m 3 ) rests on a scale. A 2.00-kg block of iron (density = kg/m 3 )is suspended from a spring scale and is completely submerged in the oil (Fig. P9.39). Find the equilibrium readings of both scales. Will the reading of the lower scale be 1. Less than weight of beaker + oil 2. Greater than weight of beaker + oil 3. Equal to weight of beaker + oil

42 Example problem: Iceberg What percentage of the volume of an iceberg can be seen above the surface of the sea? F m B f = g ρ V V f f V V V V V f = above above w = g ρ ρ = Mg = ρ f V = 1 ice V V Vg f = 1 ρ ρ f = 0.10 = 10%

43 At a distance d from an automobile the sound intensity is 10-7 W/m 2. Find intensity level. How about 3d? Or 1000 automobiles?

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true?

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true? Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which