1. (a) A block of ice of mass 0.365 kg at -15.0° C is placed in a 700 W microwave. The microwave is turned on. The ice warms, then melts to water, and then the ice water warms to 60.0° . How long does this take? Thermodynamic data for ice and water can be found in the sheet of equations. Assume that the ice/water absorbed all the microwave energy. Hint - recall that power is energy over time.
   

   (b) A thin rod made of steel is exactly 22.175 cm long at 15.0° C. A thin rod of aluminum is exactly 21.950 cm at 15.0° C. At what temperature would the rods be exactly the same length? The coefficients of linear expansion are α_steel = 11 × 10^-6/°C and α_aluminum = 23 × 10^-6/°C.
   

2. A Physics 1101 student is watering his lawn using a hose, which has a uniform diameter, as is shown in the diagram below. The student is holding the hose horizontally and the water lands 2.06 m away. The student, slightly bored, turns his chore into a real life fluid physics problem. He treats the water as a projectile and figures out the speed of the water as it leaves the hose. What is that speed? Knowing that the hose has the same cross-sectional area throughout, he determines the speed that the water enters the hose at the house. What is that speed? Knowing the speed of the water entering and leaving the hose, knowing that water has a density of 1000 kg/m³, and knowing that atmospheric pressure is 1.01 × 10⁵ Pa, he determines the water pressure at the house. What is that pressure?
   
   

3. As shown in the diagram below, a ball bearing of mass 150 g and unknown radius is pressed 15.0 cm into a spring which has a spring constant of K = 100 N/m. The ball bearing is released and rolls without slipping to the top of a semicircular hill. At the top of the hill it almost loses contact with the surface. How high is the hill?
   
   

4. A person holds the string of a yo-yo motionless and with constant tension as he lets the yo-yo drop as shown in the diagram below. The yo-yo does NOT slip as it falls. Determine the angular acceleration of the yo-yo about it's centre of mass, the linear acceleration of the yo-yo, and the tension in the string. The yo-yo has a moment of inertia of I = 2.50 × 10^-5 kg-m², an inner radius r = 1.75 cm, an outer radius R = 2.65 cm, and a mass M = 125 g.
   
   

5. The diagram below shows an arrangement of three blocks. Block 1 has a mass of 15.0 kg and is tied to a wall by a horizontal string. Block 2 has a mass of 8.0 kg and is connected to Block 3 by a string. Block 3 is also tied to a wall by a string that makes an angle θ = 38.0° with the horizontal. The tabletop is frictionless but there is friction between blocks 1 and 2. The coefficient of static friction between the two blocks is μ = 0.25. The three blocks are motionless but a slight nudge would make block 2 slide. Find the tension in each string and the mass of Block 3. Be careful with normal forces and reaction forces.
   
   

6. The wire shown below has a length of 2.00 m, a mass of 20.0 g, and is held under a tension of 100 N. When it is made to vibrate in the third harmonic, it resonates with sound in the tube. Find the two smallest lengths of the tube. Take the speed of sound in air to be 340 m/s. Sketch the standing waves on the string and in the tube.
   
   

7. The sign in the diagram below is uniform and has a mass of 31.0 kg. The wire makes an angle θ = 60.0° with the wall.
   (a) Find the tension in the wire.
   (b) Find the horizontal and vertical components of the hinge force.
   
   

8. Two rods/cylinders are standing upright on the edge of a solid disk. The system is rotating at 10.0 rad/s. Each rod has a radius of 2.00 cm, a length of 0.900 m, and a mass of 2.50 kg. The disk has a radius of 1.00 m and a mass of 14.0 kg. The rods fall outwards due to forces which are totally internal.
   (a) What is the initial moment of inertia about the axis of rotation?
   (b) What is the final moment of inertia about the axis of rotation?
   (c) What is the final rotational velocity of the system?
   
   

9. (a) Two cars are separated by 75 km of straight highway. They both head toward each other at the same time. Car A travels at a constant 45 km/h and car B travels at a constant 65 km/h. How long after they start do they pass one another? How far from car A's starting point do they pass one another?
   

   (b) Two identical incoherent spherical sound sources of the same power are distance L apart as shown in the diagram below. The sound level at point A, halfway between the speakers, is 50.0 dB. What is the sound level at point B, L/3 from one of the speakers?
   

   

10. A siren with a frequency f_s = 2000 Hz is attached to a block. The siren and block together have a mass of 2.00 kg. The block is attached to a spring of unknown spring constant K. The spring is compressed an unknown distance and then released. The siren and block oscillate back and forth. A listener hears the source as emitting a varying frequency since the siren is moving. The highest frequency that the listener hears is 2060 Hz. The listener also determines that he hears this highest frequency repeat every 1.50 seconds. The speed of sound in air is 343 m/s.
    (a) How fast is the block moving when the listener hears the highest frequency?
    (b) Where in its motion is the block when the listener hears the highest frequency?
    (c) What is the lowest frequency that the listener would hear?
    (d) Where in its motion is the block when the listener hears the lowest frequency?
    (e) What is the period and angular frequency of the block?
    (f) What is the amplitude of the displacement of the block?
    (g) What is the spring constant of the spring?
    
    

Error Propagation

Adding or Subtracting	Δ(A+B-C)= ΔA + ΔB + ΔC
Multiplying or Dividing	Δ(AB/C)= (AB/C)(ΔA/A + ΔB/B + ΔC/C)
Powers and Roots	Δ(Az) = zAz-1ΔA
Special Fuctions	sin(θ±Δθ) = sin(θ)±Δθ cos(θ) cos(θ±Δθ) = cos(θ)±Δθ sin(θ) tan(θ±Δθ) = tan(θ)±Δθ /cos2(θ) e(x±Δx) = ex±Δxex ln(x±Δx) = ln(x)±Δx/x
	Note: Δθ must be stated in radians!

Kinematics

vaverage = Δx/Δt	ωaverage = Δθ/Δt
vaverage = (vf+v0)/2	ωaverage = (ωf+ ω0)/2
aaverage = Δv/Δt	αaverage = Δω/Δt
Δx = vaveraget	Δθ = ωaveraget
Δx = v0t + ½at2	Δθ = ω0t + ½αt2
v = v0 + at	ω = ω0 + αt
v2 = (v0)2 + 2aΔx	ω2 = (ω0)2 + 2αΔθ

Translation <-> Rotation

s = Rθ

vtan = Rω

atan = Rα

ac = v2/R

Newton's Laws

ΣFx = max	ΣFy = may	fmax static = μsN	fkinetic = μkN
F = Gm1m1/R2	g(R) = GMplanet/R2	v = [GMplanet/R]½	T2 = 4π2R2/ GMcentral
G = 6.672 × 10-11 N-m2/kg2		g = 9.81 m/s2

Rolling

v_linear = v_tangential

Torque

τ = Iα

τ = r × F

τz = xFy - yFx

Moment of Inertia

Itotal = I1 + I2 + I3 ...

I = Icm + Md2

Work and Energy

	Klinear = ½mv2	Krotational = ½Iω2
Ugravity = mgh	Uspring = ½Kx2

Collisions

p = mv		Pf = Pi
v1f - v1f = -(v1i - v2i)	I = Δp = FaverageΔt

Angular Momentum

L = r × p	Lz = xpy - ypx = rpsinφ	Llinear = bmv
Lorbital = r2mω	LA = IAωA	Ltotal = L1 + L2 + L3 ...
Lfinal = Linitial

Simple Harmonic Motion

Waves

Standing Waves

If the string is fixed at both ends or air column is open at both ends

Use

Use

If the string or air column has one open end and one fixed end

Use

Use

Sound Level / Decibels / Sound Intensity

ITotal = I1 + I2 + I3 ...
ITotal = I0 × 10(β/10)	I0 = 1 × 10-12 W/m2

Doppler Shift

Use

Interference

Constructive interference (maximum amplitude) when Δx = nλ,     n = 1, 2, 3, ...

Destructive interference (zero or minimum amplitude) when Δx = nλ/2,     n = 1, 3, 5, ...

Fluids

		P2 = P2 + ρgh
Aoutvout = Ainvin		ρwater = 1000 kg/m3

Heat

		εblackbody = 1
Q = mcΔT	Qphase change = mL	cice = 2220 J/kg-K
cwater = 4190 J/kg-K
		Rseries = R1 + R2 + R3 ...
		Σ = 5.67 × 10-8 W/m2-K4

Quadratic Formula

if ax²+bx+c = 0, then

Questions? mike.coombes@kpu.ca