A smooth cube of mass m and edge length r slides with speed v non a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle θ with the horizontal. A cylinder of mass m and radius r rolls without slipping with its center of mass moving with speed v and encounters an incline of the same angle of inclination but with sufficient friction that the cylinder continues to roll without slipping. (a) Which object will go the greater distance up the incline? (b) Find the difference between the maximum distances the objects travel up the incline. (c) Explain what accounts for this difference in distances traveled.
A smooth cube of mass m and edge length r slides with speed v non a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle θ with the horizontal. A cylinder of mass m and radius r rolls without slipping with its center of mass moving with speed v and encounters an incline of the same angle of inclination but with sufficient friction that the cylinder continues to roll without slipping. (a) Which object will go the greater distance up the incline? (b) Find the difference between the maximum distances the objects travel up the incline. (c) Explain what accounts for this difference in distances traveled.
Solution Summary: The author explains the law of energy conservation for the cube and cylinder.
A smooth cube of mass m and edge length r slides with speed v non a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle θ with the horizontal. A cylinder of mass m and radius r rolls without slipping with its center of mass moving with speed v and encounters an incline of the same angle of inclination but with sufficient friction that the cylinder continues to roll without slipping. (a) Which object will go the greater distance up the incline? (b) Find the difference between the maximum distances the objects travel up the incline. (c) Explain what accounts for this difference in distances traveled.
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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.
Review 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 screen
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.
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…
Chapter 10 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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