Explanation Given: The density of silicon, ρ = 2300 kg/m 3 The initial frequency of cantilever, f o = 12 MHz The decrease in frequency, Δ f = − 50 Hz A cantilever of mass ( m ) can be modeled as a block of mass ( 1 3 m ) . The dimension of the cantilever, 4000 nm × 400 nm × 100 nm Formula Used: Density: ρ = M V Here, M is the mass and V is the volume. f = 1 2 π k m f = 1 2 π k m d f = 1 2 π ( − 1 2 ) k m − 3 / 2 d m d m = − 2 m d f f Calculation: Volume: V = 4000

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

4th Edition

ISBN: 9780133942651

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Chapter 15, Problem 54EAP

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3.) The graph shows how current I varies with potential difference V across a component X. 904 80- 70- 60- 50- I/MA 40- 30- 20- 10- 0+ 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 VIV Component X and a cell of negligible internal resistance are placed in a circuit. A variable resistor R is connected in series with component X. The ammeter reads 20mA. 4.0V 4.0V Component X and the cell are now placed in a potential divider circuit. (a) Outline why component X is considered non-ohmic. [1] (b(i)) Determine the resistance of the variable resistor. [3] (b(ii)) Calculate the power dissipated in the circuit. [1] (c(i)) State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P. [1] (c(ii)) Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).

1.) Two long parallel current-carrying wires P and Q are separated by 0.10 m. The current in wire P is 5.0 A. The magnetic force on a length of 0.50 m of wire P due to the current in wire Q is 2.0 × 10-s N. (a) State and explain the magnitude of the force on a length of 0.50 m of wire Q due to the current in P. [2] (b) Calculate the current in wire Q. [2] (c) Another current-carrying wire R is placed parallel to wires P and Q and halfway between them as shown. wire P wire R wire Q 0.05 m 0.05 m The net magnetic force on wire Q is now zero. (c.i) State the direction of the current in R, relative to the current in P.[1] (c.ii) Deduce the current in R. [2]

2.) A 50.0 resistor is connected to a cell of emf 3.00 V. The voltmeter and the ammeter in the circuit are ideal. V A 50.00 (a) The current in the ammeter is 59.0 mA. Calculate the internal resistance of the cell. The circuit is changed by connecting another resistor R in parallel to the 50.0 resistor. V A 50.00 R (b) Explain the effect of this change on R is made of a resistive wire of uniform cross-sectional area 3.1 × 10-8 m², resistivity 4.9 × 10-70m and length L. The resistance of R is given by the equation R = KL where k is a constant. (b.i) the reading of the ammeter. [2] (b.ii) the reading of the voltmeter. [2] (c) Calculate k. State an appropriate unit for your answer. [3] [2]

Chapter 15 Solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Ch. 15 - Prob. 1CQ Ch. 15 - A pendulum on Planet X, where the value of g is...Ch. 15 - FIGURE Q15.3 shows a position-versus-time graph...Ch. 15 - FIGURE Q15.4 shows a position-versus-time graph...Ch. 15 - 5. Equation 15.25 states that . What does this...Ch. 15 - A block oscillating on a spring has an amplitude...Ch. 15 - A block oscillating on a spring has a maximum...Ch. 15 - 8. The solid disk and circular hoop in FIGURE...Ch. 15 - FIGURE Q15.9 shows the potential-energy diagram...Ch. 15 - Suppose the damping constant b of an oscillator...

Ch. 15 - Prob. 11CQ Ch. 15 - 12. What is the difference between the driving...Ch. 15 - An air-track glider attached to a spring...Ch. 15 - An air-track is attached to a spring. The glider...Ch. 15 - Prob. 3EAP Ch. 15 - An object in SHM oscillates with a period of 4.0 s...Ch. 15 - What are the (a) amplitude, (b) frequency, and (c)...Ch. 15 - What are the (a) amplitude, (b) frequency, and (c)...Ch. 15 - FIGURE EX15.7 is the Position-versus-time graph of...Ch. 15 - FIGURE EX15.8 is the velocity-versus-time graph of...Ch. 15 - An object in simple harmonic motion has an...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An object in simple harmonic motion has amplitude...Ch. 15 - An air-track glider attached to a spring...Ch. 15 - 14. A block attached to a spring with unknown...Ch. 15 - 15. A 200 g air-track glider is attached to a...Ch. 15 - A 200 g mass attached to a horizontal spring...Ch. 15 - Prob. 17EAP Ch. 15 - A 1.0 kg block is attached to a spring with spring...Ch. 15 - Prob. 19EAP Ch. 15 - Prob. 20EAP Ch. 15 - A spring is hanging from the ceiling. Attaching a...Ch. 15 - 22. A spring with spring constant 15 N/m hangs...Ch. 15 - 23. A spring is hung from the ceiling. When a...Ch. 15 - Prob. 24EAP Ch. 15 - A 200 g ball is tied to a string. It is pulled to...Ch. 15 - Prob. 26EAP Ch. 15 - Prob. 27EAP Ch. 15 - Prob. 28EAP Ch. 15 - Prob. 29EAP Ch. 15 - A 100 g mass on a 1.0-m-long string is pulled 8.0...Ch. 15 - A uniform steel bar swings from a pivot at one end...Ch. 15 - Prob. 32EAP Ch. 15 - Prob. 33EAP Ch. 15 - Prob. 34EAP Ch. 15 - Vision is blurred if the head is vibrated at 29 Hz...Ch. 15 - Prob. 36EAP Ch. 15 - Prob. 37EAP Ch. 15 - a. When the displacement of a mass on a spring is...Ch. 15 - For a particle in simple harmonic motion, show...Ch. 15 - A 100g block attached to a spring with spring...Ch. 15 - A 0.300 kg oscillator has a speed of 95.4cm/s when...Ch. 15 - An ultrasonic transducer, of the type used in...Ch. 15 - Astronauts in space cannot weigh themselves by...Ch. 15 - 44. Your lab instructor has asked you to measure a...Ch. 15 - A 5.0 kg block hangs from a spring with spring...Ch. 15 - Prob. 46EAP Ch. 15 - A block hangs in equilibrium from a vertical...Ch. 15 - Prob. 48EAP Ch. 15 - 49. Scientists are measuring the properties of a...Ch. 15 - Prob. 50EAP Ch. 15 - A compact car has a mass of 1200 kg. Assume that...Ch. 15 - Prob. 52EAP Ch. 15 - Prob. 53EAP Ch. 15 - Prob. 54EAP Ch. 15 - Prob. 55EAP Ch. 15 - Prob. 56EAP Ch. 15 - Prob. 57EAP Ch. 15 - A uniform rod of mass M and length L swings as a...Ch. 15 - Prob. 59EAP Ch. 15 - 60. A 500 g air-track glider attached to a spring...Ch. 15 - Prob. 61EAP Ch. 15 - Prob. 62EAP Ch. 15 - A molecular bond can be modeled as a spring...Ch. 15 - Prob. 64EAP Ch. 15 - Prob. 65EAP Ch. 15 - Prob. 66EAP Ch. 15 - The 15 g head of a bobble-head doll oscillates in...Ch. 15 - An oscillator with a mass of 500 g and a period of...Ch. 15 - Prob. 69EAP Ch. 15 - Prob. 70EAP Ch. 15 - Prob. 71EAP Ch. 15 - Prob. 72EAP Ch. 15 - Prob. 73EAP Ch. 15 - A block ona frictionless FIGURE P15.74 to two...Ch. 15 - Prob. 75EAP Ch. 15 - Prob. 76EAP Ch. 15 - A solid sphere of mass M and radius R is suspended...Ch. 15 - A uniform rod of length L oscillates as a pendulum...Ch. 15 - Prob. 79EAP Ch. 15 - Prob. 80EAP Ch. 15 - FIGURE CP15.81 shows a 200 g uniform rod pio4ed at...

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