A baseball bat has a “sweet spot” where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle grip. Determine the location of the sweet spot of the bat shown in Fig. 11–51. Tile linear mass density of the bat is given roughly by (0.61 + 3.3 x 2 ) kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.84 m long. The desired rotation point should be 5.0 cm from the end where the bat is held. [ Hint : Where is the CM of the bat?] FIGURE 11–51 Problem 82.
A baseball bat has a “sweet spot” where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle grip. Determine the location of the sweet spot of the bat shown in Fig. 11–51. Tile linear mass density of the bat is given roughly by (0.61 + 3.3 x 2 ) kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.84 m long. The desired rotation point should be 5.0 cm from the end where the bat is held. [ Hint : Where is the CM of the bat?] FIGURE 11–51 Problem 82.
A baseball bat has a “sweet spot” where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle grip. Determine the location of the sweet spot of the bat shown in Fig. 11–51. Tile linear mass density of the bat is given roughly by (0.61 + 3.3x2) kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.84 m long. The desired rotation point should be 5.0 cm from the end where the bat is held. [Hint: Where is the CM of the bat?]
The plank AB in Fig.17-59 has a mass of 7 kg. The rollers D and E are each of mass 5kg and are 0.5 m in diameter. The plank is released from rest with roller D under the end A and the roller E, under the mass center C. assuming no slip, determine the velocity of the plank when roller E is under end B.
Show solution. Answer is 7.11 m/s
76. Round and Round Little Jay is
enjoying his first ride on a merry-go-
round. (He is riding a stationary
horse rather than one that goes up
Av at 4 = 0
%3D
and down.) A schematic view of the
merry-go-round as seen from above
is shown in Fig. 11-47a with a conve-
nient coordinate system. A bit after
the merry-go-round has started and
is going around uniformly, we start
our clock. Little Jay's position and
velocity at time t
dot and arrow. At t = 0 is the net force acting on Jay equal to zero?
If it is, write "Yes" and give a reason why you think so. If it isn't,
write “No" and specify the type of force and the object responsible
for exerting it.
FIGURE 11-47a
Problem 76.
0 are shown as a
%3D
%3D
For the next six parts, specify which of the graphs shown in
Fig. 11-47b could represent the indicated variable for Jay's motion.
If none of the graphs work, write "N."
(A
(B)
0.
-Time
Time
0.
(D)
0.
Time 0
Time
E
F
Time
Time
FIGURE 11-47b Problem 76.
(a) The x-component of Jay's velocity
(b)…
A 50-story building is being planned. It is to be 180.0 m high
with a base 46.0 m by 76.0 m. Its total mass will be about
1.8 x 107 kg, and its weight therefore about 1.8 x 10° N.
Suppose a 200-km/h wind exerts a force of 950 N/m² over
the 76.0-m-wide face (Fig. 9–80). Calculate the torque about
the potential pivot point,
the rear edge_ of the
building (where Fp acts in
Fig. 9–80), and determine
whether the building will
topple. Assume the total
force of the wind acts at
I口
the midpoint of the build-
ing's face, and that the
building is not anchored
in bedrock. [Hint: Fe in
Fig. 9-80 represents the
force that the Earth would
...
mg
exert on the building in
the case where the building
would just begin to tip.]
FIGURE 9-80 Forces on a building subjected
to wind (FA), gravity (mg), and the force FE
on the building due to the Earth if the
building were just about to tip. Problem 61.
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