Phys 5 Spring 004 Name: Final Exam April, 004 INSTRUCTIONS: a) No books, notes, or other such materials are permitted. b) You may use a calculator. c) You must solve all problems beginning with the equations on the Information Sheet provided with this test. Please write down the equation you are using, or the principle you are applying to a given situation. d) You must show your work to receive credit!!!! If a problem requires only a simple answer, you must explain your answer. Please show all of your work on the sheets provided (use the back if necessary). e) Please draw a box or a circle around each of your answers.
. A bird views itself in a convex garden mirror that is a silvered ball of radius 0 cm. The bird is located 40 cm from the mirror. (a) (0 pts.) Make a careful ray diagram to locate the image of the bird, and from this diagram determine whether the image is real or virtual, upright or inverted, magnified or reduced in size. (b) (0 pts.) If the actual height of the bird is 0 cm, find the height of its image in the mirror.
. A single-lens camera with a focal length of 50.0 mm is used to take a close-up picture of a flower that is 0 cm high. The flower is located 60 cm from the camera lens. (a) (0 pts.) What is the lens-to-film distance? (b) (0 pts.) What is the height of the flower on the film? (c) (5 pts.) If the same camera is used to photograph a very distant object, what must be the lens-to-film distance? 3
3. Light of wavelength 700 nm is incident on a narrow slit of width 0.0 mm. A screen is located 80 cm from the slit. (a) (5 pts.) Make a sketch of this situation showing the resulting light pattern on the screen. (b) (0 pts.) What is the width of the central maximum? 4
4. In a certain television set the electrons that strike the screen are accelerated from rest through a potential difference of 5,000 V over a distance of.5 cm = 0.05 m (these are typical values). (a) (5 pts.) How much work is done on an electron to accelerate it? (b) (5 pts.) What is the final speed of the electrons? (c) (5 pts.) What is the magnitude of the uniform electric field required to accomplish this? (d) (5 pts.) How must this electric field be directed relative to the motion of the electrons? Be specific! (e) (5 pts.) What is the magnitude of the acceleration of the electrons? (f) (5 pts.) Is the work done by the electric force on the electrons positive or negative? Explain your answer! (g) (5 pts.) Does the electron gain or lose electric PE during its acceleration? Explain your answer! 5
5. A flat coil of wire has 30 turns, each of radius 5 cm (area = πr ). The coil is first oriented with its plane perpendicular to a uniform magnetic field of magnitude 0.4 T. Then, in 0.050 seconds, it is rotated through 80 0 so that the plane of the coil is again perpendicular to the magnetic field (but the magnetic field points in the opposite direction through the coil). (a) (5 pts.) What is the initial (before rotation) magnetic flux through the coil? (b) (5 pts.) What is the initial (before rotation) emf in the coil? (c) (0 pts.) When the coil is rotated, what emf is induced in the coil? (d) (5 pts.) When the rotation is complete (i.e., when the coil is again at rest) what is the emf in the coil? 6
6. For the circuit shown, find (a) (0 pts.) The total current drawn from the battery. (b) (5 pts.) The voltage across the Ω resistor. (c) (0 pts.) The current in the 3 Ω resistor. (d) (5 pts.) The total power delivered by the battery. 48 V 5 Ω Ω Ω 3 Ω 7
INFORMATION SHEET F = ma a centripetal v = Φ = BA cosθ r q Φ Work = KE I = ε = N t t qq F = k V = IR ε = Blv r F L E = R = ρ ε = NBAωsin ωt A q 0 q E = k 0[ ( )] r R = R + α T T I R 0 = ( ε εback ) / WAB V V = VB VA = P = IV; P = I R = V s N = s ; P in = P q R V N out p p PE elec = W AB ; PE = W = qv Vter min al = ε Ir c = fλ q V = k R eq = R + R n = c / v ; n sin θ = n sin θ r V = Ed = + sin R eq R R θ = n c n q R C = F = qvb sin θ + = = ; f = V p q f R A image _ height q C = ε0 F = BIl sin θ M = = d object _ height p τ = NBIA sin θ C eq = C + C d sin θ = mλ ; µ 0 I = + B wire = d sin θ = ( m + ) λ C eq C C πr W = Energy = qv B solenoid = µ 0 ni a sin θ = mλ e =.6 x 0-9 C ε 0 = 8.85 x 0 - C /N-m ev =.6 x 0-9 J k = 9.0 x 0 9 N-m /C µ 0 = 4π x 0-7 T-m/A c = 3 x 0 8 m/s 8
Sign conventions for mirrors Concave: f positive Convex: f negative p is always positive q Image M Image + real + upright virtual inverted Sign conventions for lenses Convex (converging): f positive Concave (diverging): f negative p is always positive q Image M Image + real + upright virtual inverted 9