A uniform sphere of weight mg and radius r 0 is tethered to a wall by a rope of length ℓ . The rope is tied to the wall a distance h above the contact point of the sphere, as shown in Fig. 12–99. The rope makes an angle θ with respect to the wall and is not in line with the ball’s center. The coefficient of static friction between the wall and sphere is μ . ( a ) Determine the value of the frictional force on the sphere due to the wall. [ Hint : A wise choice of axis will make this calculation easy.] ( b ) Suppose the sphere is just on the verge of slipping. Derive an expression the μ in terms of h and θ . FIGURE 12–99 Problem 93.
A uniform sphere of weight mg and radius r 0 is tethered to a wall by a rope of length ℓ . The rope is tied to the wall a distance h above the contact point of the sphere, as shown in Fig. 12–99. The rope makes an angle θ with respect to the wall and is not in line with the ball’s center. The coefficient of static friction between the wall and sphere is μ . ( a ) Determine the value of the frictional force on the sphere due to the wall. [ Hint : A wise choice of axis will make this calculation easy.] ( b ) Suppose the sphere is just on the verge of slipping. Derive an expression the μ in terms of h and θ . FIGURE 12–99 Problem 93.
A uniform sphere of weight mg and radius r0 is tethered to a wall by a rope of length ℓ. The rope is tied to the wall a distance h above the contact point of the sphere, as shown in Fig. 12–99. The rope makes an angle θ with respect to the wall and is not in line with the ball’s center. The coefficient of static friction between the wall and sphere is μ. (a) Determine the value of the frictional force on the sphere due to the wall. [Hint: A wise choice of axis will make this calculation easy.] (b) Suppose the sphere is just on the verge of slipping. Derive an expression the μ in terms of h and θ.
A cube of side l rests on a rough floor. It is subjected to a
steady horizontal pull F, exerted a distance h above the floor
as shown in Fig. 9-79. As Fis increased, the block will either
begin to slide, or begin to tip over.
Determine the coefficient of static
friction us so that (a) the block
begins to slide rather than tip;
(b) the block begins to tip.
[Hint: Where will the normal
force on the block act if it tips?]
h
FIGURE 9–79
Problem 60.
(II) An iron bolt is used to connect two iron plates together. The bolt must withstand shear forces up to about 3300 N. Calculate the minimum diameter for the bolt, based on a safety factor of 7.0.
(III) A door 2.30 m high and 1.30 m wide has a mass of
13.0 kg. A hinge 0.40 m from the top and another hinge
0.40 m from the bottom each support half the door's weight
(Fig. 9–69). Assume that the center
of gravity is at the geometrical
center of the door, and determine
40 cm
2.30 m
the horizontal and vertical force
components exerted by each hinge
on the door.
-1.30 m-
F40 cm
FIGURE 9-69
Problem 29.
Chapter 12 Solutions
Physics for Scientists & Engineers with Modern Physics [With Access Code]
Essential University Physics: Volume 1 (3rd Edition)
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