Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 18.1, Problem 1bTH
What is the direction of the wheel’s
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Portfolio Problem 4. Consider two identical springs, each with natural length
and spring constant k, attached to a horizontal frame at distance 2l apart. Their
free ends are attached to the same particle of mass m, which is hanging under
gravity. Let z denote the vertical displacement of the particle from the hori-
zontal frame, so that z < 0 when the particle is below the frame, as shown in
the figure. The particle has zero horizontal velocity, so that the motion is one
dimensional along z.
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0
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(a) Show that the total force acting on the particle is
X
F-mg k-2kz 1
(1.
l
k.
(b) Find the potential energy U(x, y, z) of the system such that U
x = : 0.
= O when
(c) The particle is pulled down until the springs are each of length 3l, and then
released. Find the velocity of the particle when it crosses z = 0.
In the figure below, a semicircular conductor of radius R = 0.260 m is rotated about the axis AC at a constant rate of 130 rev/min. A uniform magnetic field of magnitude 1.22 T fills the entire region below the axis and is directed out of the page.
R
Pout
(a) Calculate the maximum value of the emf induced between the ends of the conductor.
1.77
v
(b) What is the value of the average induced emf for each complete rotation?
0
v
(c) How would your answers to parts (a) and (b) change if the magnetic field were allowed to extend a distance R above the axis of rotation? (Select all that apply.)
The value in part (a) would increase.
The value in part (a) would remain the same.
The value in part (a) would decrease.
The value in part (b) would increase.
The value in part (b) would remain the same.
The value in part (b) would decrease.
×
(d) Sketch the emf versus time when the field is as drawn in the figure. Choose File No file chosen
This answer has not been graded yet.
(e) Sketch the emf…
Portfolio Problem 2. A particle of mass m slides in a straight line (say along i)
on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The
=
particle is subject to a constant force F = -mai, with a > 0.
While sliding on the surface, the particle is also subject to a friction force
v
Ff
= -m fo
= −m fov,
with fo > 0, i.e., the friction force has constant magnitude mfo and is always
opposed to the motion. We also assume fo 0, and solve it to find v(t) and x(t).
How long does it take for the particle to come to a stop? How far does it travel?
(b) After coming to a stop, the particle starts sliding backwards with negative
velocity. Write the equation of motion in this case, and solve it to find the time
at which the particle returns to the original position, x = 0. Show that the final
speed at x 0 is smaller than Vo.
=
Express all your answers in terms of a, fo and Vo.
Chapter 18 Solutions
Tutorials in Introductory Physics
Ch. 18.1 - What is the direction of the angular velocity of...Ch. 18.1 - What is the direction of the wheel’s angular...Ch. 18.1 - Rank the magnitudes of the centripetal...Ch. 18.1 - For each situation described below, describe a...Ch. 18.1 - The equation a0andaR0 is not a correct vector...Ch. 18.2 - Prob. 1aTHCh. 18.2 - Draw an extanded freebody diagram for the ruler at...Ch. 18.2 - Rank the magnitudes of all the forces on your...Ch. 18.2 - Is the rotation of the ruler about the pivot in a...Ch. 18.2 - In the boxes at right, indicate the direction of...
Ch. 18.2 - Check that your descriptions of the motion of the...Ch. 18.2 - Parts iiv refer to the instant shown in the...Ch. 18.2 - Suppose that each force shown above is exerted for...Ch. 18.3 - What does this observation imply about the net...Ch. 18.3 - Draw an extended free-body diagram for theboard in...Ch. 18.3 - Would the board remain at rest in this case?...Ch. 18.3 - On the figure above, mark the approximate location...Ch. 18.3 - Is the amount of mass of the system (clay and...Ch. 18.3 - A T-shaped sheet of uniform thickness has a...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- = Portfolio Problem 1. A particle of mass m is dropped (i.e., falls down with zero initial velocity) at time t 0 from height h. If the particle is subject to gravitational acceleration only, i.e., a = −gk, determine its speed as it hits the ground by solving explicitly the expressions for its velocity and position. Next, verify your result using dimensional analysis, assuming that the general relation is of the form v = khag³m, where k is a dimensionless constant.arrow_forwardReview Conceptual Example 2 before attempting this problem. Two slits are 0.158 mm apart. A mixture of red light (wavelength = 693 nm) and yellow-green light (wavelength = 567 nm) falls on the slits. A flat observation screen is located 2.42 m away. What is the distance on the screen between the third-order red fringe and the third-order yellow- green fringe? m = 3 m = 3 m= 0 m = 3 m = 3 Fringes on observation screenarrow_forwardIn the figure below, a semicircular conductor of radius R = 0.260 m is rotated about the axis AC at a constant rate of 130 rev/min. A uniform magnetic field of magnitude 1.22 T fills the entire region below the axis and is directed out of the page. In this illustration, a wire extends straight to the right from point A, then curves up and around in a semicircle of radius R. On the right side of the semicircle, the wire continues straight to the right to point C. The wire lies in the plane of the page, in a region of no magnetic field. Directly below the axis A C is a region of uniform magnetic field pointing out of the page, vector Bout. If viewed from the right, the wire can rotate counterclockwise, so that the semicircular part can rotate into the region of magnetic field. (a) Calculate the maximum value of the emf induced between the ends of the conductor. V(b) What is the value of the average induced emf for each complete rotation? Consider carefully whether the correct answer is…arrow_forward
- A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.20 cm and 1.00 103 turns/meter (see figure below). The current in the solenoid changes as I = 6.00 sin(120t), where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time. (Do not include units in your answer.) =arrow_forwardA coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 1.80 cm and 1.00 103 turns/meter (see figure below). The current in the solenoid changes as I = 5.00 sin(120t), where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time. (Do not include units in your answer.) =arrow_forwardWhich vowel does this graph represent (”ah,” “ee,” or “oo”)? How can you tell? Also, how would you be able to tell for the other vowels?arrow_forward
- Concept Simulation 26.4 provides the option of exploring the ray diagram that applies to this problem. The distance between an object and its image formed by a diverging lens is 5.90 cm. The focal length of the lens is -2.60 cm. Find (a) the image distance and (b) the object distance.arrow_forwardA bat is flying toward a cave wall at 27.0 m/s. What is the frequency of the reflected sound that it hears, assuming it emits sound at 52.0 kHz? The speed of sound is 341.5 m/s. Multiple Choice о 60.9 kHz О 56.5 kHz о 61.3 kHz О 56.1 kHzarrow_forwardCompare the slope of your Data Table 2 graph to the average wavelength (Ave, l) from Data Table 2 by calculating the % Difference. Is the % Difference calculated for the wavelength in Data Table 2 within an acceptable % error? Explain why or why not?arrow_forward
- The slope of a graph of velocity, v, vs frequency, f, is equal to wavelength, l. Compare the slope of your Data Table 1 graph to the average wavelength (Ave, l) from Data Table 1 by calculating the % Difference.arrow_forwardExamine the slope of the line on the graph created using the data in Data Table 4 of Period, T2 vs L, the slope of the line is a constant containing the acceleration due to gravity, g. Using the slope of your line, determine the experimental value for g. Compare the value you determined for g from the slope of the graph to the expected value of 9.81 m/s2 by calculating the percent error.arrow_forwardFrom your examination of the graph created using the data in Data Table 4 of Period, T vs √L . What would you determine is the relationship between the period of a pendulum and the length of a pendulum?arrow_forward
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