Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 1.2, Problem 1lT
Description of Motion:
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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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(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 1 Solutions
Tutorials in Introductory Physics
Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - A. In the space below, sketch a possible ticker...Ch. 1.1 - B. Together with your classmates, take your ticker...Ch. 1.1 - C. Based on your observations of your tape segment...
Ch. 1.1 - D. Review your earlier interpretation of the speed...Ch. 1.1 - E. Suppose you selected two widely separated dots...Ch. 1.2 - The computer program assumes a particular...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - How are the motions in parts C and D similar? How...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion: Move toward the detector...Ch. 1.2 - How do the acceleration graphs for F, G, and H...Ch. 1.2 - Description of Motion: Initially move away from...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - The term decelerate is often used to indicate that...Ch. 1.3 - Draw vectors on your diagram that represent the...Ch. 1.3 - B. In the space at right, compare the velocities...Ch. 1.3 - Consider the change in velocity vector between two...Ch. 1.3 - Use the definition of acceleration to draw a...Ch. 1.3 - Does the acceleration change as the ball rolls up...Ch. 1.3 - Generalize your results thus far to answer the...Ch. 1.3 - Choose two successive points. In the space at...Ch. 1.3 - In the space at right, draw a vector to represent...Ch. 1.3 - Choose a point before the turnaround and another...Ch. 1.3 - Suppose that you had chosen the turnaround as one...Ch. 1.3 - In the space at right, draw a vector that...Ch. 1.4 - Prob. 1aTCh. 1.4 - If you were to choose a different origin for the...Ch. 1.4 - On a separate part of your paper, copy the...Ch. 1.4 - Suppose you were to choose a new point on the...Ch. 1.4 - On a separate part of your paper, copy the...Ch. 1.4 - Suppose the object started from rest at point E...Ch. 1.4 - At several points on each of the diagrams below,...Ch. 1.5 - The second diagram at right shows the positions of...Ch. 1.5 - The picture of the spaceships and shuttle from the...Ch. 1.5 - Prob. 1cTCh. 1.5 - Spaceship C moves so as to remain a fixed distance...Ch. 1.5 - Consider the following statement: "The...Ch. 1.5 - Prob. 1fTCh. 1.5 - Describe the motion of the car and the truck...Ch. 1.5 - Complete the diagram at right by drawing the car...Ch. 1.5 - Use your completed diagram to sketch average...Ch. 1.5 - During a small time interval t from just before to...
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- = 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
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