Final Examination

One 8½ × 11 sheet containing formulas is allowed.

Please start each question on a new page in your booklet.

1. When sewer pipes are blocked, city engineers often use the following trick to find where the blockage has occurred. They go to an unblocked end as shown below and play a pure single frequency tone into the open end. They change the frequency until they find the lowest frequency that causes a resonance or standing wave. In this particular case they find that f = 4.95 Hz. The speed of sound in air is 340 m/s.
   (a) What is the distance to the blockage?
   (b) Sketch the standing wave.
   (c) What is the next highest frequency that produces a standing wave?
   

2. The diagram below shows a Velocity Selector used to allow only charged particles with a desired velocity to pass though. The velocity selector consists of a magnetic field B and an electric field E at right angles to one another. At one end is a hole that allows charged particles with various speeds to enter. At the other end is a small hole to let out particles that have not changed velocity. The charged particles have very little mass.
   (a) Sketch the path that a negative charge would take if its speed is too large.
   (b) Sketch the path that a negative charge would take if its speed is too small.
   (c) Sketch the path that a positive charge would take if its speed is too large.
   (d) Sketch the path that a positive charge would take if its speed is too small.
   (e) If B = 0.200 T and E = 1200 N/C, what is the velocity that a negative charge must have to pass through both holes?
   (f) If B = 0.200 T and E = 1200 N/C, what is the velocity that a positive charge must have to pass through both holes?
   

3. (a) Find the x and y components of the net electric field at point A. We know that Q₁ = 5.0 μC, Q₂ = –3.0 μC, r₁ = 0.20 m, r₂ = 0.15 m, and θ = 30.0°.
   

   (b) Find the x and y components of the net magnetic field at point B. We know that I₁ = 5.0 A into the paper, I₂ = 3.0 A out of the paper, r₁ = 0.20 m, r₂ = 0.15 m, and θ = 30.0°.

   

4. During a hockey game, a puck is shot across the ice and deflects off the boards as shown in the diagram below. The angle of incidence is the same as the angle of reflection and equals θ = 27º. The speed of the puck just before and after the collision is 80 km/h. The puck is in contact with the boards for 0.0015 s. The puck has a mass of 0.330 kg. Find the magnitude and direction of the average force acting on the puck during the collision.
   

5. A person places an object 40 cm from a converging lens that has a focal length of 30 cm. Where will the image form? Characterize the final image. The person moves the lens around (not the object) and discovers that he can find another position for the lens that produces an image which is the same distance from the object as before although the image is a different size.   How far is the object from the lens in this case? Characterize the final image.

6. (a) Diagram (i) below presents the velocity versus time graph of a particle. Sketch the corresponding position versus time graph. Indicate t_A on your sketch.
   (b) Diagram (ii) below presents the position versus time graph of a particle. Sketch the corresponding velocity versus time graph. Indicate t_A on your sketch.
   (c) Diagram (iii) below presents the velocity versus time graph of a particle. When does the particle turn around? Explain.
   (d) In Diagram (iii), what is the average velocity in Segment B?
   (e) In Diagram (iii), what is the displacement between t = 2.0 s and t = 6.0 s?
   
   

7. Three blocks are connected by strings as shown in the diagram below. The blocks have mass μ₁ = 0.200 kg, μ₂ = 1.000 kg, and μ₃ = 0.400 kg. The coefficients of friction between the middle block and the table are μ_s = 0.25 and μ_k = 0.15. Find the acceleration of the blocks.
   

8. A student is working with the circuit shown in the diagram below. She uses an ammeter and finds that the current through the branch with the 300-Ω resistor to be I = 0.050 A.
   (a) What is the voltage drop across the 300-Ω resistor?
   (b) What is the voltage drop across the 150-Ω resistor?
   (c) What is the current through the 150-Ω resistor?
   (d) What is the current through the 100-Ω resistor?
   (e) What is the voltage drop across the 100-Ω resistor?
   (f) What is the emf of the battery?
   

9. A rollercoaster filled with people is moving with speed v_A at point A on a flat part of the track. Ahead is a circular hill on the track of radius R = 25.0 m. At point B, at the very top of the hill, the people feel one-third as heavy as normal. How fast does v_A have to be for that to have happened? Ignore friction and air resistance.
   

10. Two boys are playing catch. Initially the boys are 15.0 m apart. The first boy makes a weak pitch at a velocity of v = 8.50 m/s at an angle of 27º. The other boy starts running at constant speed as soon as the other boy throws the ball. How fast must the second boy run in order to catch the ball? Assume he catches the ball at the same height it left the first boy.
    

Useful Formulas

		sin(2θ) = 2sin(θ)cos(θ)
	G = 6.672 × 10-11 N-m2/kg2
W=FLcos(θ)	K=½mv2	U = mgh
Wnc = Ef – Ei	E = K + U
		k = 8.99 × 109 N-m2/C2
V=IR		P= IV
F = qvBsin(φ)	r = mv/qB	½mv2 = qΔV
F = ILBsin(φ)		μ0 = 4π × 10 -7 T-m/A
If string is fixed at both ends, or air column is open at both ends,
If string or air column has one open end and one fixed end,

Quadratic Equation
Given the formula , the solutions are

Questions? mike.coombes@kwantlen.ca