1. An object is placed 48.0 cm from a converging lens which has a focal length of 30.0 cm.
   (a) Characterize the image formed. Include where the image is, whether it is real or virtual, erect or inverted, and its magnification.
   (b) Neatly and accurately, provide a sketch of the image using the Principle Ray Technique.
   (c) Draw an eye on your drawing to indicate where an observer would have to be to see the image.
   

2. (a) A string of mass 32.0 g, length 3.15 m, and under a tension of 12.0 N, has the standing wave pattern shown in the diagram below.
   (i) What is the speed of a wave on this string?
   (ii) What is the frequency of vibration that produced this wave?
   
   

   (b) The diagram below shows an end-on view of two wires which are 40.0 cm apart. The wire on the left carries a current I_out = 2.15 Amps out of the page. What would have to be the direction and magnitude of I₂ for the net magnetic field at point A to be zero. Point A is 15.0 cm from the wire on the left.
   

   

3. Find the equivalent resistance of the circuit below. Find the current, potential drop, and power through each resistor.
   
   

4. A particle of mass m = 75.0 g and charge q = 60.0 μC is moving through a box at a speed of v = 2400 m/s. In the box is an electric field E_up = 5000 N/C and an unknown magnetic field B_in. If the acceleration of the charge is zero, what is B_in?
   

5. At point A, in the diagram below, a block has a velocity of 5.00 m/s. Between points A and C, the surface is frictionless but from point C to D the coefficient of friction is μ_k = 0.71. The last part of the hill is straight and makes an angle θ = 15.0° with the horizontal.
   (a) It is known at point B that the apparent weight of the block is only 7/8^th of its true weight. What is the radius of curvature, R, of the hill? Hint - consider the energies of points A and B.
   (b) The block comes to a complete stop at point D. How long is the path from C to D? Hint - consider the energies of points A and D.
   
   

6. Two blocks undergo a totally inelastic collision at point A on a frictionless surface. Block 1 has a mass of 22.0 kg and a speed of 12.2 m/s directed as shown. Block 2 has a mass of 17.0 kg and a speed of 13.7 m/s.
   (a) What is the velocity of the blocks after the collision?
   (b) How much kinetic energy is lost in the collision?
   
   

7. A block slides from rest at point A over a frictionless surface to point B where it is launched into the air. It later lands at point C. The heights in the diagram are h_A = 2.75 m and h_B = 1.15 m. The given angle is θ = 125.0°.
   (a) How fast is the block moving at point B?
   (b) How far is point C from point B?
   (c) How long is the block in air?
   
   

8. The small asteroids are arranged in outer space as shown in the diagram below. The masses of the asteroids are m_A = 1.25 × 10¹⁰ kg, m_B = 1.78 × 10¹⁰ kg, and m_C = 3.56 × 10¹⁰ kg. The separation of the asteroids is given by r₁ = 2500 m and r₂ = 4250 m. The asteroids also have charge Q_A = 0.300 C, Q_B = 0.700 C, and Q_C = 1.400 C . Find the magnitude and direction of the acceleration of asteroid A at the instant shown below.
   

9. Two blocks of mass M₁ = 5.00 kg and M₂ = 7.50 kg and on a surface where the coefficient of kinetic friction is μ = 0.30 . The second block is being pulled by a force F = 75 N. Both blocks have the same acceleration.
   (a) Find the magnitude of the acceleration.
   (b) Find the tension in the string connecting the blocks.
   
   

10. (a) The graph below shows the position versus time curve for a moving block.
    (i) At what time(s) is the velocity of the block zero?
    (ii) What is the instantaneous velocity of the block at t = 3.50 s?
    

    

    (b) The graph below shows the velocity versus time curve for a moving block.
    (i) At what time(s) is the block turning around?
    (ii) What is the displacement of the block between t = 3.00 s and t = 9.00 s?
    (iii) What is the average velocity between t = 4.50 s and t = 7.50 s?
    

    

Formulas

Kinematics

		vaverage = ½(vf+v0)
Δx = vaveraget	Δx = v0t + ½at2	v = v0 + at
		g = 9.81 m/s2

Newton's Laws

ΣFx = max	ΣFy = may	fmax static = μsN	fkinetic = μkN
G = 6.672 × 10-11 N-m2/kg2

Work and Energy

W = FΔxcos θ = FxΔx

Wnc = ΔK + ΔP

K = ½mv2

P = mgh

Collisions

m1v1f + m2v2f = m1v1i + m2v2i	I = mvf - mvi = FaverageΔt
p = mv

Coulomb's Law and Electric Fields

F = qE	k = 8.99 × 109 N-m2/C2

Electric Circuits

V = IR	Rseries = R1 + R2 + ...
P = IR2 = IV = V/R2		Vvoltmeter = IG(Rcoil +Rmultiplier)

Magnetic Fields

F = qvBsinφ
F = ILBsinφ		μ0 = 4π × 102 T-m/A

Standing Waves

Reflection, Refraction, Mirrors and Lenses

θincident = θreflected	n1sinθ1 = n2sinθ2
	f = ½R
	f = + concave mirrors, converging lens f = - convex mirrors, divergin lens o = + object on incident side i = + image on incident side of mirror, on transmission side of lens i = - image behind mirror, on incident side of lens

Quadratic Formula

if ax²+bx+c = 0, then

Questions? mike.coombes@kpu.ca