Problem 64
Problem 66.
64 A wagon is being pulled at constant speed up a slopeθ
by a rope that makes an angleφwith the vertical. (a) Assuming
negligible friction, show that the tension in the rope is given by the
equation
T=
sinθ
sin(θ+φ)mg,(b) Interpret this equation in the special cases ofφ= 0 andφ=
180 ◦−θ. .Solution, p. 1038
65 The angle of repose is the maximum slope on which an object
will not slide. On airless, geologically inert bodies like the moon or
an asteroid, the only thing that determines whether dust or rubble
will stay on a slope is whether the slope is less steep than the angle
of repose.
(a) Find an equation for the angle of repose, deciding for yourself
what are the relevant variables.
(b) On an asteroid, wheregcan be thousands of times lower than
on Earth, would rubble be able to lie at a steeper angle of repose?
.Solution, p. 1038
66 When you’re done using an electric mixer, you can get most
of the batter off of the beaters by lifting them out of the batter with
the motor running at a high enough speed. Let’s imagine, to make
things easier to visualize, that we instead have a piece of tape stuck
to one of the beaters.
(a) Explain why static friction has no effect on whether or not the
tape flies off.
(b) Analyze the forces in which the tape participates, using a table
in the format shown in subsection 3.2.6.
(c) Suppose you find that the tape doesn’t fly off when the motor is
on a low speed, but at a greater speed, the tape won’t stay on. Why
would the greater speed change things? [Hint: If you don’t invoke
any law of physics, you haven’t explained it.]
67 Show that the expression|v|^2 /rhas the units of acceleration.68 A plane is flown in a loop-the-loop of radius 1.00 km. The
plane starts out flying upside-down, straight and level, then begins
curving up along the circular loop, and is right-side up when it
reaches the top. (The plane may slow down somewhat on the way
up.) How fast must the plane be going at the top if the pilot is to
experience no force from the seat or the seatbelt while at the top of
the loop?√69 Find the angle between the following two vectors:xˆ+ 2ˆy+ 3ˆz
4 ˆx+ 5yˆ+ 6ˆz.Hint, p. 1031√234 Chapter 3 Conservation of Momentum